This article presents a new design of self-triggered impulsive control (STIC) for prescribed-time stability (PTS) of nonlinear systems. A prescribed-time convergent function is proposed to determine the impulsive control strength together with the information of the impulsive interval. Different from previous impulsive control strategies, the impulsive control with designable strength is implemented under a non-Zeno self-triggering mechanism (STM) with enforced bounded execution times and the triggering times established by a comparison system. The involvement of the upper bound of the impulsive interval in both control strength and STM not only renders the closed-loop prescribed-time stable but also ensures decreasing impulsive strengths as the time approaches the prescribed time. The validity of the proposed STIC scheme is verified by the application to prescribed-time synchronization of reaction-diffusion neural networks (RDNNs) and numerical examples.

This article studies the stability problem of uncertain nonlinear systems by self-triggered impulsive control (STIC) methods with nonlinear impulses. With the help of comparison principle, a class of self-triggered mechanisms (STMs) is proposed, where the next triggering instant is given in explicit form with lower communication occupations. Moreover, different from the existing STIC results, the effect of nonlinear impulses is fully considered in the design of STIC strategies in this article, by which the constraints associated with the impulsive control gain can be relaxed. Under such STIC strategies, some sufficient conditions for local asymptotical stability (LAS) of uncertain nonlinear systems are put forward and the estimation of convergence region is provided, with simple structure for easy implementation. In addition, there is no Zeno behavior for the designed STM. Finally, two simulation examples are given to illustrate the validity and advantage of our theoretical results.

This paper investigates the Lyapunov stability problem for switched systems involving stable and unstable modes under event-triggered impulsive control. By constructing multiple Lyapunov functions coupled with average dwell-time methods, some sufficient conditions on Lyapunov stability of switched systems involving stable and unstable modes are provided under event-triggered impulsive control. The designed event-triggered impulsive control strategy is mode-dependent, and Zeno behavior is eliminated. Then, with the construction of a connection between average dwell-time scheme and total dwell time of unstable modes, a relationship between mode-dependent event-triggered mechanism, system dynamics, and switching law is established. It plays a key role in designing event-triggered impulsive control with easy implementation. Moreover, this paper applies the theoretical results to the nonlinear switched system involving dual modes, in which an event-triggered impulsive control strategy is designed for the stability of the switched system. Finally, three numerical examples are given to verify the validity of the proposed results.

This paper addresses the stability of time-varying systems using event-triggered impulsive control. A new event-triggered mechanism with time-varying structure is proposed, ensuring global asymptotic stability and avoiding Zeno behavior. The relationship between impulse actions, time delay, and system dynamics is explored, with two examples confirming the results.

This paper deals with finite-time stabilization (FTS) of nonlinear systems subject to actuator saturation. We present an analytical method to design the finite-time controller such that the FTS of the system can be guaranteed in the presence of actuator saturation. Moreover, a certain interrelation among the saturation bound, the system structure, and the controller parameters is established. Based on such a relationship, the settling time (ST) and the domain of attraction (DA) can both be estimated in an easily verifiable manner, which are ignored in many existing results of actuator saturation. Moreover, it is shown that the parameter of the designed controller can provide a tradeoff between the estimations of the ST and the DA by adjusting the controller parameters. All the results are illustrated in simulations. Note to Practitioners—Actuator saturation, a phenomenon where the control input exceeds the limits of an actuator, plays a crucial role in control theory and its applications. In control systems, actuator saturation can lead to performance degradation, instability, and even system failure if not properly addressed, such as Chornobyl nuclear power plant accident and the YF-22 crash incident. Note that in the presence of actuator saturation, most existing results focus on Lyapunov stability or finite-time boundedness, which makes it challenging to guarantee that the system converges to equilibrium within a finite time. This paper was motivated to break through this bottleneck and solve the FTS problem. Unlike the existing saturation results, we first decompose the system based on controllability. Then a straightforward controller design is proposed for the controllable part, while constraints on the system structure are provided for the uncontrollable part. Based on such conditions, not only is the estimation of the DA easily obtained, but the corresponding ST estimation is also derived. The obtained results in this paper are of great significance for providing a more general and easily achievable design for saturated control input. And these results are applied to various industries, such as aerospace, automotive, mobile robotics technology, and industrial automation.

This paper investigates the problem of globally exponential stability (GES) for impulsive switched systems via a hybrid switching strategy. First, a switching law combining state-dependent and time-dependent (dwell time) switching strategies is presented in the framework of impulse action. On the basis of the switching law, some GES criteria are proposed by using multiple Lyapunov function technique. A potential relationship among system parameters, impulse action including impulse amplitude and impulse frequency, and the combined switching law is established, which is of vital importance to achieving GES. In addition, when the impulse action involved in switched system is given in terms of stabilizing impulse, the impulsive controller including impulsive gains and impulsive frequency can be designed with the help of the proposed switching law to guarantee the stability of the addressed system. Finally, a simulation example is demonstrated to verify the validity of the proposed switching law and corresponding results. Note to Practitioners—This paper is motivated by the control problem of hybrid systems under a discontinuous environment in practical terms, such as optimal control models in economics, motor controllers in electric vehicles, and traffic flow control in intelligent transportation systems. Due to the hybrid nature of switched systems, they are challenging to compare independently with continuous or discrete systems. Therefore, this paper thoroughly investigates the stability control of nonlinear switched systems in the framework of impulse action. State-dependent switching strategy is an effective control method for on-demand switching. However, existing results often require continuous monitoring of system states, leading to significant computational and communication resource consumption. To address this issue, a hybrid switching strategy including state-dependent and time-dependent switching is firstly proposed for impulsive switched systems in this paper. A relationship among system parameters, impulse action, and the combined switching law is established. Then easy-checked exponential stability criteria are presented based on the proposed hybrid switching strategy. The results demonstrate that the use of hybrid switching strategy significantly reduces switching frequencies and saves control costs while ensuring system stability. In future work, we will consider to explore the application of this novel and efficient switching strategy to study the finite-time stability of hybrid systems, particularly in the presence of inevitable external uncertainties in practical environments.

This paper investigates the problems of finite-time stabilization ( FTS) and finite-time contractive stabilization ( FTCS) for nonlinear systems by designing a novel class of hybrid control consisting of aperiodically intermittent control ( APIC) and impulsive control ( IC). Different from the single APIC, our proposed hybrid control specifically introduces IC on the intervals without control input in APIC. It shows that IC in hybrid control may not only flexibly shorten the length of the intervals with continuous control input, but also alleviate the design pressure of gain of APIC. Based on the hybrid control, some Lyapunov-based criteria are derived to guarantee the FTS and FTCS, where a potential relationship between system structure, APIC law, and impulse actions is established. Specifically, some linear matrix inequalities ( LMIs) based criteria are presented to design the hybrid control gains. As an application, the theoretical results are extended to the finite-time state estimation of complex networks involving the unavailable network states. With the available measurement outputs, the hybrid state estimator involving both APIC and IC is proposed. Finally, three numerical examples are provided to illustrate the effectiveness of our results.Note to Practitioners—Unlike the Lyapunov stability results, the transient performances described by FTS and FTCS can be quantitatively guaranteed in the finite-time sense and have better applicability for the practical engineering requirements. This paper was motivated to solve FTS and FTCS problems. To guarantee the FTS and FTCS, a novel class of hybrid control is designed, which integrates the advantages of APIC and IC. Compared with the single APIC, the introduction of IC may reduce the dependence on the continuous control input in APIC, which significantly reduces the energy consumption of communication. The introduction of IC can also alleviate the design pressure of APIC to some extent. Hence, some easy-checked FTS and FTCS criteria are presented based on the proposed hybrid control. In practical applications, the theoretical results are extended to investigate the finite-time state estimation of complex networks considering unavailable network states. Utilizing the available measurement outputs, the corresponding hybrid state estimator consisting of APIC and IC is constructed. Finally, note that the impulsive transmission of ball motion is considered to further illustrate the practicability of our proposed results. In the future work, our proposed hybrid control strategy can be applied in other practical projects, such as the finite-time control of omnidirectional mobile robot.

This article focuses on the self-triggered impulsive control (STIC) problem of nonlinear systems subject to exogenous disturbances. Specifically, with the construction of a novel self-triggered mechanism (STM) containing the information of state and disturbance, the next release time of impulsive control signal is attained accompanied with each update of the impulsive control task, without real-time monitoring of the state. On the strength of the suggested STM and by means of Lyapunov-based approaches, some sufficient conditions are proposed to guarantee the input-to-state practical stability (ISpS) for the considered system, while avoiding the possible Zeno phenomenon. Especially, the design of mechanism and control gain is explored for a class of nonlinear control systems with the help of matrix inequalities. Two examples are provided to demonstrate the feasibility of the proposed results.

This study investigates the stability of reaction-diffusion systems (RDSs) under impulsive disturbances using an event-triggered impulsive control method. Our key contribution is providing Zeno-free conditions for the event-triggered mechanism (ETM), which is crucial due to the potential for impulsive disturbances to trigger the sampling threshold earlier than expected, leading to Zeno behavior. We address this challenge by deriving conditions that ensure the ETM operates without Zeno behavior, essential for practical control implementation. We further derive several sufficient conditions for the asymptotic stability of RDSs based on impulsive control theory. Special cases with specific disturbance rules are also discussed, offering a broader understanding of system stability under various conditions. To demonstrate the applicability of our theoretical findings, we apply our control strategies to an atmospheric pollution model. A numerical example is provided to validate the effectiveness of our approach and to offer theoretical guidance for real-world environmental pollution control.

This article investigates the local synchronization for delayed complex dynamical networks (CDNs) under self-triggered impulsive control (STIC) approaches involving delays. With the help of Lyapunov-Razumikhin methods and comparison principle, some design criteria of STIC strategies ensuring local synchronization for delayed CDNs with delayed impulses are provided, and Zeno behavior can be avoided. Compared with the existing results on synchronization of CDNs under STIC, in this article, time delays in both continuous and discrete system dynamics are well considered. Moreover, the proposed self-triggered mechanism (STM) is an explicit expression, under which the next triggering instant can be derived directly, with simple structure and easy implementation. Finally, two numerical examples are provided to validate the proposed theoretical criteria.

In this article, we devote to investigate the self-triggered impulsive control (STIC) approaches for input-to-state stability (ISS) of nonlinear T-S fuzzy delay systems. With the help of the Lyapunov–Razumikhin technique, an ISS-type comparison principle is proposed. The designed self-triggering mechanism (STM) can predict the next impulse instant only using the current state information, different from the existing event-triggered results that need a continuous state monitor. Based on such an STM, some impulsive controller design schemes for ISS of T-S fuzzy delay systems are provided. In addition, non-Zeno behavior can be guaranteed automatically without extra limitations. Finally, two simulations are provided to verify the effectiveness of the proposed theoretical results.

This article investigates the local exponential stabilization (LES) for a class of nonlinear systems involving unmeasurable states subject to actuator saturation, where a novel kind of impulsive observer-based saturated impulsive control (SIC) is proposed. Some sufficient criteria for LES are derived drawing on impulsive control theory and saturated control methods. In order to ensure LES under the dual complexity of unmeasurable states and actuator saturation, an improved set inclusion condition for the convex combination approach is put forward, under which the saturation nonlinearity including the observer state can be linearized. Moreover, a convex optimal algorithm is given to estimate the domain of attraction as large as possible. As an application, the proposed theoretical results are applied to leader–follower synchronization of complex networks involving unmeasurable states and actuator saturation. The corresponding synchronization impulsive observer-based SIC strategy is presented. Finally, the efficacy of the results is illustrated by the proposed two examples.

This article investigates the event-triggered impulsive control (ETIC) problem for a class of nonlinear time-delay systems subject to exogenous disturbances. An original event-triggered mechanism (ETM) which utilizes the information of system state and external input is constructed based on Lyapunov function approach. To achieve the input-to-state stability (ISS) of the considered system, some sufficient conditions are presented, in which the underlying relationship among ETM, exogenous input, and impulse action is established. Furthermore, the possible Zeno behavior induced by the proposed ETM is excluded simultaneously. As an application, the design criterion of ETM and impulse gain is put forward for a class of impulsive control systems with delay according to the feasibility of some linear matrix inequalities (LMIs). Finally, two examples with numerical simulations are provided to confirm the effectiveness of the developed theoretical results, where the synchronization issue of delayed Chua's circuit is considered.

This article studies Lyapunov stability for nonlinear systems based on discrete-time self-triggered impulsive control (STIC). With the help of comparison approach, some Lyapunov-based sufficient conditions guaranteeing nonZeno behavior and global asymptotic stability of nonlinear systems under STIC are derived. Different from the existing self-triggered mechanisms using implicit expressions to compute the next impulse instant, which may result in computational burden, we propose a novel discrete-time self-triggered mechanism (STM) by which the next impulse instant can be predicted directly by the information of the comparison system. Moreover, the resulting algorithm is easy to be implemented. It is shown that the designed STIC strategy can not only achieve a tradeoff between computational complexity, communication resource usage and control performance, but also has strong robustness and flexibility. Finally, an illustrative simulation is provided showing the effectiveness of the results.

In the framework of input saturation, this article studies the problem of finite-time synchronization (FTS) of a class of complex dynamical networks. By designing different classes of saturated controllers, two types of FTS criteria, including leader-follower synchronization and leaderless synchronization, are presented, respectively. A potential relationship between the saturation structure, the settling time, and the domain of attraction is established, which is crucial to achieve FTS. It shows that the saturation structure not only affects the estimation of domain of attraction but also possibly changes the settling time for FTS. Two numerical examples are presented to illustrate the effectiveness of the proposed results.

This article focuses on the stability issue of switched network control systems (SNCSs) under deception attacks described by a Bernoulli process with unknown probability distribution. The false information in deception attacks is unknown but bounded and may be state dependent or state independent. By means of the input-to-state stability (ISS) tool and the convex combination method, an improved lemma is first developed for SNCSs, which facilitates the derivations of our results. After that, some attack-independent sufficient conditions for the ISS of SNCSs are obtained for mode-dependent average dwell time switching and stochastic switching, respectively. Different from existing results, the concerned switching contributes to the stability of SNCSs, which benefits the ISS performance of SNCSs even though the unknown deception attacks cause all subsystems to be non-ISS. The proposed results provide an effective solution with strong robustness to deal with unknown deception attacks or denial-of-service attacks.

In the framework of impulsive control, this article deals with the lag synchronization problem of neural networks involving partially unmeasurable states, where the time delay in impulses is fully addressed. Since the complexity of external environment and uncertainty of networks, which may lead to a result that the information of partial states is unmeasurable, the key problem for lag synchronization control is how to utilize the information of measurable states to design suitable impulsive control. By using linear matrix inequality (LMI) and transition matrix method coupled with dimension expansion technique, some sufficient conditions are derived to guarantee lag synchronization, where the requirement for information of all states is needless. Moreover, our proposed conditions not only allow the existence of unmeasurable states but also reduce the restrictions on the number of measurable states, which shows the generality of our results and wide-application in practice. Finally, two illustrative examples and their numerical simulations are presented to demonstrate the effectiveness of main results.

The issue of finite-time synchronization (FTS) of complex dynamical networks (CDNs) is investigated in this article. A new control strategy coupling weak finite-time control and finite times of impulsive control is proposed to realize the FTS of CDNs, where the impulses are synchronizing and restricted by maximal impulsive interval (MII), differing from the existing results. In this framework, several global and local FTS criteria are established by using the concept of impulsive degree. The times of impulsive control in the controllers and the settling time, which are all dependent on initial values, are derived optimally. A technical lemma is developed, reflecting the core idea of this article. A simulation example is given to demonstrate the main results finally.

This article investigates the problem of globally exponential stability (GES) for a class of nonlinear impulsive switched systems. By means of impulsive control theory and Lyapunov function method, some GES criteria for the addressed systems are obtained by a state-dependent switching (SDS) law. Different from the traditional SDS approach which is generally based on the framework of continuous state space, our results are presented in the framework of impulse action. On the one hand, it is shown that by virtue of SDS approach, the GES can still be achieved even all impulsive subsystems are unstable. On the other hand, it is shown that when the continuous dynamics of the subsystems are destabilizing, the impulse action may contribute to the stability as well as the SDS action if there is a lower restriction on the impulse frequency; when the continuous dynamics of the subsystems are stabilizing, under the help of SDS action, the destabilizing (disturbance) effect of impulses is allowed in the absence of frequent impulses. Two numerical examples are presented to illustrate the effectiveness of the obtained results.

Based on energy-based multiple Lyapunov functions approaches, this article concerns with stabilization and$\mathcal {H}_{\infty }$control for switched uncertain port-controlled Hamiltonian (SUPCH) systems with mode-dependent average dwell time (MDADT) switching. To better deal with the uncertainties of each mode, an improved MDADT scheme along with corresponding constraint conditions is established, and the criterion on globally uniformly asymptotical stability is presented for SUPCH systems in unforced form under the new MDADT mechanism. Subsequently, based on mode-dependent state feedback (MDSF) strategies, the sufficient conditions are derived for stabilization of SUPCH systems. Furthermore, to solve$\mathcal {H}_{\infty }$control problem for SUPCH systems with disturbances, a set of MDSF controllers are constructed, and the$\mathcal {H}_{\infty }$control criterion is obtained by the improved MDADT scheme. Finally, as an application, some simulations on a switched nonlinear RLC circuit system with structural uncertainties are carried out by the proposed control strategies.

This article presents a self-triggered impulsive framework for group consensus of multiagent systems (MASs). Two types of self-triggered delayed impulsive control schemes are proposed to regulate impulsive protocols with sensing and actuation delays, respectively. Here, the Lyapunov-based and comparison-system-based approaches are constructed to achieve the iterative updates of impulse sequences with flexibility, especially the upper bound or average interval of impulsive periods is not restricted explicitly. In addition, several sufficient criteria for multigroup consensus of MASs with sensing and actuation delays are presented, where the correlation inequalities between trigger parameters, time delays, and control strengths are established to promote the co-design of impulsive controller and self-triggering algorithm. The Zeno behavior could be successfully eliminated. It is shown that the presented self-triggered schemes do not necessitate continuous or periodic event-detections and the interaction for neighboring agents works in an impulsive manner, which significantly saves the resource consumption of communication and control. Finally, two numerical examples illustrate the effectiveness of the proposed schemes.

This article studies global exponential stabilization almost surely (GES a.s.) of linear delayed systems with random impulses using dynamic output quantized control. The impulse intensity is uncertain and switches according to acrlong TP, where both stabilizing and destabilizing impulses may coexist. A new Lyapunov–Krasovskii functional approach is developed to gain sufficient criteria for ensuring the GES a.s.. It is shown that the random impulse has positive effect on the stability, even though the norm of the impulse intensity is larger than one. It is discovered that the acrlong DOQC is not necessary to stabilize the system without impulse. The effectiveness and advantages of the theoretical analysis are verified by numerical simulations.

This article focuses on prescribed-time control for nonlinear switched systems using event-triggered impulsive control. Taking into account different characteristic among each mode, two types of mode-dependent event-triggered mechanisms are presented with mode-dependent Lyapunov functions and tunable exponential parameters, which substantially reduce the update times of controller. It shows that, the interevent times, under the designed mode-dependent event-triggered mechanism, have a uniform lower bound and then do not exhibit Zeno behavior. Further, using Lyapunov approach, some sufficient conditions for prescribed-time stability are obtained, where a relationship among triggering parameter, impulse strength, and prescribed time is established explicitly. As an application, the proposed methods are proved to be applicable to switched control systems, where a class of LMI-based hybrid control approaches, including switching control and event-triggered impulsive control, is developed. The effectiveness of our presented event-triggered impulsive control is illustrated through two examples.

This article mainly explores the local input-to-state stability (LISS) property of a class of nonlinear systems via a saturated control strategy, where both the external disturbance and impulsive disturbance being fully considered. In terms of the Lyapunov method and inequality techniques, some sufficient conditions under which the system can be made LISS are proposed, and the elastic constraint relationship among saturated control gain, rate coefficients, external disturbance, and domain of initial value is revealed. Moreover, the optimization design procedures are provided with the hope of obtaining the estimates of admissible external disturbance and domain of initial value as large as possible, where the corresponding saturated control law can be designed by solving LMI -based conditions. In the absence of an external disturbance, the locally exponential stability (LES) property can also be presented with a set of more relaxed conditions. Finally, two examples are presented to reveal the validity of the obtained results.

The dynamical study of continuous-/discontinuous-time fractional-order neural networks (FONNs) has been thoroughly explored, and several publications have been made available. This study is designed to give an exhaustive review of the dynamical studies of multidimensional FONNs in continuous/discontinuous time, including Hopfield NNs (HNNs), Cohen-Grossberg NNs, and bidirectional associative memory NNs, and similar models are considered in real ( [Formula: see text]), complex ( [Formula: see text]), quaternion ( [Formula: see text]), and octonion ( [Formula: see text]) fields. Since, in practice, delays are unavoidable, theoretical findings from multidimensional FONNs with various types of delays are thoroughly evaluated. Some required and adequate stability and synchronization requirements are also mentioned for fractional-order NNs without delays.

Considered the stimulation of tumor necrosis factor as an impulsive control, an apoptosis network is modeled as a state-dependent impulsive Boolean network (SDIBN). Making cell death normally means driving the trajectory of an apoptosis network out of states that indicate cell survival. To achieve the goal, this article focuses on the pinning controller design for set reachability of SDIBNs. To begin with, the definitions of reachability and set reachability are introduced, and their relation is illustrated. For judging whether the trajectory of an SDIBN leaves undesirable states, a necessary and sufficient condition is presented according to the criteria for the set reachability. In addition, a series of algorithms is provided to find all possible sets of pinning nodes for the set reachability. Note that attractors containing in all undesirable states are studied to make SDIBNs set reachable via controlling the smallest states. For the purpose of determining pinning nodes for one-step set reachability, the Hamming distance is presented under scalar forms of states. Pinning nodes with the smallest cardinality for the set reachability are derived by deleting some redundant nodes. Compared with the existing results, the state feedback gain can be obtained without solving logical matrix equations. The computation complexity of the proposed approach is lower than that of the existing methods. Moreover, the method of designing pinning controllers is used to discuss apoptosis networks. The experimental result shows that apoptosis networks depart from undesirable states by controlling only one node.

This article studies the local exponential synchronization synthesis problem of directed Lur'e networks with coupling time-varying delay under the distributed impulsive control subject to actuator saturation. First, by utilizing proof by contradiction, impulsive comparison principle, and latest improved convex hull representation of saturation function, some delay-independent sufficient criteria for local exponential synchronization are presented in the form of bilinear matrix inequalities. Meanwhile, a novel method with less conservatism is developed to estimate the domain of attraction, which is radically different from the traditional method by means of contractive invariant set. Second, optimization problems constrained by the transformed linear matrix inequalities are established to acquire the maximum estimates of both the domain of attraction and average impulsive interval (AII), which are conveniently solved by the YALMIP toolbox in MATLAB software. Finally, a numerical simulation is rendered to demonstrate the effectiveness and advantages of the proposed theoretical results.

This article focuses on stability analysis of delayed reaction-diffusion neural-network models with hybrid impulses based on the vector Lyapunov function. First, several properties of a vector Halanay-type inequality are given to be the key ingredient for the stability analysis. Then, the Krasovskii-type theorems are established for sufficient conditions of exponential stability, which removes the common threshold of impulses in each neuron subsystem at every impulse time. It shows that the stability of neural networks can be retained with hybrid impulses involved in neural networks, and the synchronization of neural networks can be achieved by designing an impulsive controller, which allows the existence of impulsive perturbation in some nodes and time. Finally, the effectiveness of theoretical results is verified by numerical examples with a successful application to image encryption.

This article studies the problem of finite-time stability (FTS) and finite-time contractive stability (FTCS) for nonlinear impulsive systems, where the possibility of time delay in impulses is fully considered. Some sufficient conditions for FTS/FTCS are constructed in the framework of Lyapunov function methods. A relationship between impulsive frequency and the time delay existing in impulses is established to reveal FTS/FTCS performance. As an application, we apply the theoretical results to finite-time state estimation of neural networks, including time-varying neural networks and switched neural networks. Finally, two illustrated examples are given to show the effectiveness and distinctiveness of the proposed delay-dependent impulsive schemes.

This article studies the problem of prescribed-time stabilization for nonlinear systems, in which impulses are cautiously regulated not only to stabilize the system in a finite-time sense but also to adjust the settling time to fit the prescribed terminal time. By fetching and utilizing positive effect of impulses, constrains on continuous flows are effectively relaxed for prescribed-time stabilization of nonlinear systems. Meanwhile, different from traditional prescribed-time approaches, where continuous flows of the system are generally required to be globally stable, it shows in this article that even systems involving unstable flows can be prescribed-time stabilized via the proposed impulsive regulation, but as a tradeoff, a constrained initial condition is needed for controller design. Thus, the main functions of impulsive regulation in this article are balancing unstable dynamics of the system, and regulating the settling time to fit the prescribed terminal time. As an application, the proposed impulsive regulation scheme is exploited in prescribed-time stabilization of affine dynamical systems involving uncertain input noises. Two examples, including the one focusing on the spin stabilization of spacecrafts, are given to verify the results.

This article applies output-based event-triggered control (ETC) strategies to nonlinear systems involving impulses and investigates the problem for globally exponential stability (GES). The impulses are not directly related to events and two kinds of control schemes (static and dynamic ETC) are fully considered, respectively. Moreover, the stabilizing and destabilizing impulses can coexist (i.e., hybrid impulses). By employing properties of impulsive system theory and Lyapunov conditions, some theoretical conditions for GES and non-Zeno behavior are derived under static and dynamic event-triggered mechanism, respectively. And the results for stability are different but complementary to each other. Based on the linear matrix inequality, the design criteria of expected triggered mechanism and control gains are derived. Finally, two numerical examples containing simulations are given to demonstrate the effectiveness of the proposed control strategy.

This article considers the cluster synchronization of coupled genetic oscillator networks (GONs) with proportional delay via the event-triggered pinning impulsive control (ETPIC). First, a novel Lyapunov-dependent event-triggered rule for impulsive functional differential equation that includes proportional delay is proposed by means of a new auxiliary function and the improved Lyapunov–Razumikhin method, which is different from the previous results. And then, a Lyapunov-dependent ETPIC rule is first designed, which integrates the pinning control with the established event-triggered impulsive control. On this basis, some new cluster synchronization criteria for coupled GONs with proportional delay are derived in the light of linear matrix inequalities. Note that the triggering impulsive instant is determined by the designed ETPIC rule, and only a fraction of nodes of each cluster are controlled at each triggering instant according to the designed algorithm. Finally, a numerical example is provided to show the effectiveness of the proposed approach.

This article focuses on input-to-state stability (ISS) of impulsive time-delay systems where the hybrid effect of impulses with time-dependent multiple jump maps in different subsystems is fully considered. By virtue of M-matrix and vector Lyapunov function, some theorems for ISS are established for Krasovskii-type conditions which avoid the common threshold of impulses in subsystems and allow the simultaneous existence of stable and unstable continuous subdynamics. If the time intervals between impulses are bounded, the ISS of time-delay systems can be ensured even though hybrid impulses exist in each subsystem, which determines the robustness of stable time-delay systems with respect to hybrid impulses. The unstable time-delay systems with different subdynamics can be stabilized in input-to-state-stability sense by involving hybrid impulses. In addition, several extended criteria are presented to bridge the results derived via vector Lyapunov function, scalar Lyapunov function, and comparison principle. At last, the theoretical results are validated by numerical example and a simplified model of sewage treatment tank.

Finite-time stability (FTS) for nonlinear systems with delayed impulses is characterized in terms of Lyapunov method, where time delays in impulses occur between two consecutive impulse instants. Some Lyapunov-based sufficient conditions are presented to guarantee FTS, where a relationship among the system structure, the delayed impulses, and the settling time is established. For stabilizing impulses with time delays, the design of impulse time sequence is proposed, under which the estimation of settling time relying on the impulse jump, the time delays, and the initial condition is obtained. For destabilizing impulses with time delays, some constraints of the impulse time sequence affected by two different size scopes of time delays are put forward. Our results show that delayed impulses may contribute to or destroy the FTS and lead to different estimations of the settling time. The analysis is illustrated by two numerical examples.

The article investigates the practical finite-time stability (PFTS) issue of continuous-time nonlinear systems with disturbance. Some extended Lyapunov results for semi-global/global PFTS, including attraction domain and settling time estimation are obtained based on a relaxed Lyapunov condition. Especially, for systems with stabilizing delayed impulses, a new scheme of delayed impulsive control involving a finite number of impulses is proposed to realize semi-global and/or global PFTS, where the minimum number of impulses can be explicitly designed in terms of initial states. Optimal delayed impulsive control design is provided in different situations to yield the minimum settling time estimation. Several numerical examples illustrate the validity of the obtained results finally.

Quasi-consensus tracking problems of uncertain multi-agent systems are investigated in this paper. By integrating impulsive control theory with event-triggered mechanism, a new hybrid event-triggered impulsive consensus protocol is presented, under which the information transmission of agents occurs at a sequence of state-dependent instants. Based on Lyapunov method, several quasi-consensus criteria of uncertain multi-agent systems are constructed, as well as the relation among control gains, event parameters, consensus error level, and convergence rate is established. It shows that the hybrid event-triggered control strategy benefits to save the energy cost of information transmission and control cost between agents compared with the time-triggered scheme, and it is effective to achieve quasi-consensus tracking objective of considered systems. Finally, the Zeno behavior is shown to be ruled out, and some simulation examples are proposed to demonstrate the validity of the theoretical analysis.

This article investigates input-to-state stability (ISS) and integral ISS (iISS) of nonlinear impulsive systems based on the event-triggered impulsive control (ETIC) strategy, where the impulse sequence is generated by some predesigned event conditions. Unlike traditional event-triggered control, ETIC means that the controller is activated only when some state-dependent event conditions are triggered and moreover, there is not any control transmission between two consecutive triggered impulse instants. Event-triggered impulses are usually regarded as a class of state-dependent impulses, where the event-triggered mechanism (ETM) is an impulse generator. By using the ETIC strategy, some Lyapunov-based criteria are established, which can effectively avoid infinitely fast triggering behavior and guarantee ISS/iISS of nonlinear impulsive systems. Then, the theoretical results are applied to nonlinear system, where a class of ETMs and impulsive control gain are derived with the help of LMIs. Finally, two numerical examples are presented to illustrate the validity of our control strategies.

In this article, the finite-time synchronization problem of delayed complex dynamical networks (CDNs) with impulses is studied, where two types of impulses, namely, synchronizing impulses and desynchronizing impulses, are fully considered, respectively. Since the existence of impulses makes the discontinuity of the states, which means that the classical result for finite-time stability is inapplicable in such a case, the key challenge is how to guarantee the finite-time stability and estimate the settling time in impulse sense. We apply impulsive control theory and finite-time stability theory to CDNs and establish some sufficient conditions for finite-time synchronization, where two kinds of memory controllers are designed for synchronizing impulses and desynchronizing impulses, respectively. Moreover, the upper bounds for settling time of synchronization, which depends on the impulse sequences, are effectively estimated. It shows that the synchronizing impulses can shorten the settling time of synchronization; conversely, the desynchronizing impulses can delay it. Finally, the theoretical analysis is verified by two simulation examples.

This article studies the event-triggered finite-time stabilization problem of nonlinear switched systems in which the time derivatives of Lyapunov functions of modes are indefinite. Based on a mode-dependent average dwell time constraint and event-triggered impulsive control (ETIC) strategy, a new type of the mode-dependent event-triggered mechanism (MDETM) which can efficiently avoid Zeno behavior for switched systems is presented. Some Lyapunov-based criteria for finite-time stability (FTS) and finite-time contractive stability (FTCS) are obtained, respectively, where a relationship between the prescribed bound and event-triggered mechanism is established. Then, we apply these proposed ETIC strategies to impulsive switched systems and design a class of LMI-based MDETMs to guarantee the FTS/FTCS property. Finally, the effectiveness of presented ETIC strategies is illustrated by two examples.

In this paper, Lyapunov-Razumikhin technique, design of state-dependent switching laws, a fixed point theorem and variational methods are employed to derive the existence and the unique existence results of globally exponentially stable (positive) stationary solution of delayed reaction–diffusion cell neural networks under Dirichlet zero boundary value, including the global stability criteria in the classical meaning. Next, sufficient conditions are proposed to guarantee the global stability invariance of ordinary differential systems under the influence of diffusions. New theorems show that the diffusion is a double-edged sword in judging the stability of diffusion systems. Besides, an example is constructed to illuminate that any non-zero constant equilibrium point must be not in the phase plane of dynamic system under Dirichlet zero boundary value, or it must lead to a contradiction. Next, under Lipschitz assumptions on active function, another example is designed to prove that the small diffusion effect will cause the essential change of the phase plane structure of the dynamic behavior of the delayed neural networks via a Saddle point theorem. Finally, a numerical example illustrates the feasibility of the proposed methods. It is worth mentioning that some interesting mathematical problems are originally put forward in the last chapter.

This article deals with the exponential synchronization problem for complex dynamical networks (CDNs) with coupling delay by means of the event-triggered delayed impulsive control (ETDIC) strategy. This novel ETDIC strategy combining delayed impulsive control with the event-triggering mechanism is formulated based on the quadratic Lyapunov function. Among them, the event-triggering instants are generated whenever the ETDIC strategy is violated and delayed impulsive control is implemented only at event-triggering instants, which allows the existence of some network problems, such as packet loss, misordering, and retransmission. By employing the Lyapunov-Razumikhin (L-R) technique and impulsive control theory, some sufficient conditions with less conservatism are proposed in terms of linear matrix inequalities (LMIs), which indicates that the ETDIC strategy can guarantee the achievement of the exponential synchronization and eliminate the Zeno phenomenon. Finally, a numerical example and its simulations are presented to verify the effectiveness of the proposed ETDIC strategy.

In this article, we are concerned with the input-to-state stability (ISS) problem for a class of nonlinear systems with exogenous disturbances, where the states of the system are not fully available. Based on the idea of event-triggered control (ETC) strategy, a novel event-triggered mechanism (ETM) is designed to reduce the burden of the communication and controller updating with guaranteed performance requirement. Correspondingly, an observer-based impulsive controller coupled with sample control is proposed such that the controlled system is ISS under the designed ETM. Moreover, the possible accumulations of triggered instants (i.e., Zeno behavior) in the proposed control strategy are excluded. The controller gains and ETM parameters are co-designed by solving linear matrix inequalities (LMIs). Finally, a numerical example is provided to illustrate the effectiveness of the obtained theoretical results.

In this paper, we address the adaptive neural tracking control problem for a class of uncertain switched stochastic nonlinear pure-feedback systems with nonlower triangular form. The significant design difficulty is the completely unknown nonlinear functions with all state variables that can neither be directly estimated by radial basis function (RBF) neural networks (NNs) nor be eliminated by the traditional backstepping technique. To achieve the control objective of this paper, a common state-feedback controller for all subsystems is first systematically constructed by using the common coordinate transformation, the variable separation technique, and the universal approximation capability of RBF NNs. Then the stability analysis shows that the semi-global bounded in probability of the whole closed-loop switched system can be obtained and the desired tracking performance can also be insured under a class of switching signals with the average dwell time property. Finally, simulation results are given to demonstrate the effectiveness of the obtained control scheme.

In this article, the stabilization problem of mismatched disturbance systems with or without time delays is studied via observed-based sliding mode control (SMC). Two kinds of SMC schemes for systems with time delay and without time delay are considered, respectively. When time delay is addressed in the system, an SMC strategy is structured via disturbance observer, where the unknown external disturbances are supposed to be generated by an exogenous dynamic. When time delay is not addressed, an SMC approach is designed in which the unknown external disturbances are assumed to tend to a constant steady state in infinite time. Sufficient conditions for stability of the corresponding sliding motion are derived by using Lyapunov–Krasovskii functional and Lyapunov function approach, respectively. Our results can be applied when the bound of the disturbances are unmeasured or unknown. Two simulation examples are shown to illustrate the proposed methods.

We review the research on complex dynamical networks (CDNs) with impulsive effects. We provide a comprehensive and intuitive overview of the fundamental results and recent progress of CDNs with impulsive effects, where impulsive effects are considered from two aspects, i.e., impulsive control and impulsive perturbation. Five aspects of CDNs with impulsive effects are surveyed, including synchronizing impulses, desynchronizing impulses, adaptive-impulsive synchronization, pinning impulsive synchronization, and CDNs with stochastic and impulsive effects. Finally, conclusions and some future research directions are briefly addressed.

Impulsive control of nonlinear delay systems is studied in this paper, where the time delays addressed may be the constant delay, bounded time-varying delay, or unbounded time-varying delay. Based on the impulsive control theory and some analysis techniques, a new theoretical result for global exponential stability is derived from the impulsive control point of view. The significance of the presented result is that the stability can be achieved via the impulsive control at certain impulse points despite the existence of impulsive perturbations which causes negative effect to the control. That is, the impulsive control provides a super performance to allow the existence of impulsive perturbations. In addition, we apply the theoretical result to the problem of impulsive control of delayed neural networks. Some results for global exponential stability and synchronization control of neural networks with time delays are derived via impulsive control. Three illustrated examples are given to show the effectiveness and distinctiveness of the proposed impulsive control schemes.

This article investigates global exponential synchronization almost surely (GES a.s.) of complex networks (CNs) with node delay and switching topology. By introducing transition probability (TP) and mode-dependent average dwell time (MDADT) to the switching signal, the considered model is more practical than the systems with average dwell-time (ADT) switching. Controllers with both impulsive effects and actuator fault feedback are considered. New analytical techniques are developed to obtain sufficient conditions to guarantee the GES a.s. Different from the existing results on the synchronization of switched systems, our results show that the GES a.s. can still be achieved even in the case that the upper bound of the dwell time (DT) of uncontrolled nodes is very large and the lower bound of the DT of controlled nodes is very small. Numerical examples demonstrate the effectiveness and the merits of the theoretical analysis.

For the teleoperation system consisting of single-master and multislave (SMMS) manipulators, the Takagi-Sugeno (T-S) fuzzy technique has been adopted in this article to represent the nonlinear system and to approximate its nonlinearities effectively. With respect to the master-slave interactions, a decentralized leaderless communication topology has been considered for the control design with time delays in signal transmission. The corresponding forward and backward delays among the master and slaves were assumed to be asymmetric and varying with time. Moreover, to improve the tracking performance of the master and slaves, the decentralized controller is implemented with force feedback strategy to form the closed-loop teleoperation system. For the stability analysis, the fuzzy Lyapunov-Krasovskii functionals with some membership function dependent matrices were employed to guarantee the asymptotical stability of the proposed T-S fuzzy SMMS teleoperation system. By employing free-matrix-based inequality, some sufficient conditions were derived and expressed in terms of linear matrix inequalities. Finally, numerical simulations are performed on flexible joint manipulators to illustrate the validity of the proposed strategy.

In this article, the quasi-synchronization and Hopf bifurcation issues are investigated for the fractional-order quaternion-valued neural networks (QVNNs) with time delay in the presence of parameter mismatches. On the basis of noncommutativity property of quaternion multiplication results, the quaternion network has been split as four real-valued networks. A synchronization theorem for fractional-order QVNNs is derived by employing suitable Lyapunov functional candidate; furthermore, the bifurcation behavior of the hub-structured fractional-order QVNNs with time delay has been investigated. Finally, two numerical examples are provided to demonstrate the effectiveness of the theoretical results.

We study the stability properties of switched stochastic neural networks (SSNNs) with time-varying delays whose subsystem is not necessarily stable. We introduce state-dependent switching (SDS) as a tool for stability analysis. Some SDS laws for asymptotic stability and p th moment exponentially stable are designed by employing Lyapunov-Krasovskii (L-K) functional and Lyapunov-Razumikhin (L-R) method, respectively. It is shown that the stability of SSNNs with time-varying delays composed of unstable subsystems can be achieved by using SDS law. The control gains in the designed SDS laws can be derived by solving the LMIs in derived stability criteria. Two numerical examples are provided to demonstrate the effectiveness of the proposed SDS laws.

This paper investigates the leader-following consensus problem of multiagent systems using a distributed event-triggered impulsive control method. For each agent, the controller is updated only when some state-dependent errors exceed a tolerable bound. The control inputs will be carried out by actor only at event triggering impulsive instants. According to the Lyapunov stability theory and impulsive method, several sufficient criteria for leader-following consensus are derived. Also, it is shown that continuous communication of neighboring agents can be avoided, and Zeno-behavior can be excluded in our schema. The results are illustrated through several numerical simulation examples.

We establish global exponential stability theorems for impulsive delay differential systems with flexible impulse frequency. Since impulses often occur instantaneously, intermittently, or irregularly, it is possible that impulses occur with high frequency in some time-domains, and with low frequency in some others, which means that it is not always reasonable for existing results to make assumptions on common lower (or upper) bound of impulsive intervals in the analysis of stability. We propose a new approach which is based on impulsive control theory, the method of auxiliary functions, and linear matrix inequality technique to solve the problem of flexible impulse frequency. This paper mainly focuses on the stability analysis from the impulsive perturbations point of view, that is, the system subjects to destabilizing impulses. In this category, our developing results admit the existence of irregular impulsive intervals. It shows a fact that even there are some time intervals with high impulse frequency, the stability of delay system can still be guaranteed provided that the impulsive intervals with low impulse frequency satisfy certain conditions. Two numerical examples and their simulations are given to show the effectiveness of the proposed approach.

This paper investigates the dynamical multisynchronization and static multisynchronization problem for delayed coupled multistable neural networks with fixed and switching topologies. To begin with, a class of activation functions as well as several sufficient conditions are introduced to ensure that every subnetwork has multiple equilibrium states. By constructing an appropriate Lyapunov function and by employing impulsive control theory and the average impulsive interval method, several sufficient conditions for multisynchronization in terms of linear matrix inequalities (LMIs) are obtained. Moreover, a unified impulsive controller is designed by means of the established LMIs. Finally, a numerical example is presented to demonstrate the effectiveness of the presented impulsive control strategy.

In this paper, a class of recurrent neural networks with discrete and continuously distributed delays is considered. Sufficient conditions for the existence, uniqueness, and global exponential stability of a periodic solution are obtained by using contraction mapping theorem and stability theory on impulsive functional differential equations. The proposed method, which differs from the existing results in the literature, shows that network models may admit a periodic solution which is globally exponentially stable via proper impulsive control strategies even if it is originally unstable or divergent. Two numerical examples and their computer simulations are offered to show the effectiveness of our new results.

In this paper, a class of impulsive interval neural networks with discrete and distributed time-varying delays is discussed. Several new sufficient conditions are obtained ensuring the existence, uniqueness, and global exponential stability of periodic solution (i.e., stationary oscillation) for the addressed models based on inequality analysis techniques. The obtained results can be checked easily by the linear matrix inequality control toolbox in MATLAB. Finally, two numerical examples are given to show the effectiveness of our results.