For providing a more accurate description of probabilistic and model uncertainties, this paper studies the stabilization of G-stochastic complex networks (SCNs-G), where the normality assumption on noise is removed by accounting for non-Gaussian G-noise. Unlike prior intermittent event-triggered control (IE-TC), a novel asynchronous hierarchical-triggered intermittent controller (AHTIC) is designed, where the asynchronous self-triggered law determines the switching between intermittent control (IC) intervals and rest intervals, while the asynchronous dynamic event-triggered mechanism (E-TM) governs the sampling rule within the control intervals. The hierarchical-triggered feature enables the proposed AHTIC strategy to respond adaptively to unanticipated events while improving energy efficiency. Note that the sublinear expectation framework that the SCNs-G stems from, results in the existing IE-TC stabilization results inapplicable. Subsequently, a novel G-Lyapunov functional with assisting functions is constructed, and a new analytical technique is introduced to tackle the challenges arising from sublinear expectations. Specifically, the stability analysis relies on the estimation of sublinear expectations for several integrals relating to sampling errors, dynamic terms, and system states, which in turn enables the derivation of less conservative stability conditions. By means of Lyapunov functional method, and G-stochastic analysis techniques, two types of exponential stabilization criteria, including mean-square and quasi-sure exponential stability, for the control system are developed. Finally, the effectiveness of theoretical results is validated by numerical simulations on autonomous land vehicle networks.

This article studies the synchronization problem in a class of coupled stochastic nonlinear systems featuring time-varying and non-strongly connected coupling structures. In order to solve the problem posed by non-strong connectivity, an innovative hierarchical method is proposed, which enables us to study the synchronization in a layered manner. For achieving synchronization, actual controllers are constructed through the application of new coordinate transformations and the design of virtual controllers. Furthermore, by leveraging graph theory techniques and Lyapunov method, the mean square exponential synchronization criterion is derived. Finally, the theoretical results are applied to coupled Chua’s circuits, and their effectiveness is confirmed via numerical simulations. Note to Practitioners—This article is motivated by the synchronization results of stochastic strict-feedback nonlinear systems. At present, most studies concentrate on simple single-input single-output stochastic nonlinear systems, yet interconnected multi-input multi-output stochastic nonlinear systems hold greater significance in real-world scenarios. This research expands its focus to the coupling structures between interconnected stochastic nonlinear systems, which are not only time-varying but also allow non-strongly connected topological forms. This extension significantly enhances the practical application of traditional single-input single-output nonlinear systems. Additionally, considering the non-strongly connected nature, an innovative hierarchical approach is proposed. This method allows for layer-by-layer synchronization analysis, concurrently broadening the application of graph theory in this field. In the process of ensuring the synchronization of each layer, successful construction of fourth-order Lyapunov functions and actual controllers was achieved through appropriate variable substitutions and virtual controllers design. Overall, this paper provides a new perspective and methodology for the synchronization analysis and research of interconnected stochastic nonlinear systems.

This paper addresses the problem of quasi-synchronization for a class of heterogeneous fractional-order dynamical networks with time-varying couplings. Our proposed approach, called delay-dependent hybrid impulsive control, considers the network’s topology and utilizes Lyapunov functions for synchronization analysis. We employ a graph-theoretic method to construct these Lyapunov functions, including a novel time-varying graph-theoretic Lyapunov function (TGLF) that changes with the network’s structure and state variables. However, applying fractional derivatives to the TGLF poses challenges, as the general Leibniz formula and chain rule do not apply. To overcome this obstacle, we establish a new fractional derivative rule for time-varying-coefficient convex functions. We also introduce a new lemma for a fractional-order delayed impulsive differential inequality to analyze the quasi-stability and instability of impulse-free systems. By combining the TGLF and the fractional-order delayed impulsive differential inequality, we derive criteria for quasi-synchronization and estimate the allowable error bounds. Finally, we provide numerical examples to demonstrate the effectiveness of our proposed approach.Note to Practitioners—Most quasi-synchronization results of complex dynamical networks are mainly supported by the traditional quadratic Lyapunov function or the graph-theoretic Lyapunov function. However, these functions are only effective for networks with fixed couplings, which limits the application scope of the Lyapunov method. Aiming at the case of time-varying couplings, this paper proposes a novel time-varying graph-theoretic Lyapunov function that changes with the network’s structure and state variables. By applying the new fractional derivative rule of this function, we shall obtain quasi-synchronization criteria of heterogeneous fractional-order complex dynamical networks with time-varying couplings by using delay-dependent hybrid impulsive control. To verify the application of theoretical results, a generalization of the fractional-order power system is provided, and we realize its quasi-synchronization theoretically and numerically.

This paper focuses on the quasi-synchronization of heterogeneous hybrid stochastic delayed networks (HHSDNs), in which pinning aperiodically intermittent discrete observation control (PAIDOC) strategy is imposed on the networks. During control intervals, PAIDOC is based on discrete-time state observations and is implemented to a fraction of the network nodes, which is an extension of existing literature. In light of stochastic analysis theory and Lyapunov method, we establish improved quasi-synchronization criteria. Compared with previous quasi-synchronization results on HHSDNs, the piecewise continuous, time-varying, and indefinite functions replace the constant coefficient of the upper bound estimation for the operator of a Lyapunov function in the available literature, i.e., it can be positive or negative along time evolution, which shows wider applications of our results. Especially, our results can be directly applied to examine the quasi-synchronization problem via PAIDOC based on the average control rate. Subsequently, some easily-verified quasi-synchronization criteria are presented and a detailed algorithm about how to design suitable PAIDOC is provided. In the end, the theoretical result is applied to spring-mass-damper systems and numerical examples are presented.Note to Practitioners—This paper was motivated by existing results on pinning aperiodically intermittent control about the quasi-synchronization. The existing results mainly require the control method to be continuously sampled and control all nodes of the network, which is difficult to be implemented in practical application. This paper designs a novel hybrid control method named pinning aperiodically intermittent discrete observation control. In addition, we established a lower conservative differential inequality first, which is significantly conducive to analyzing the quasi-synchronization of complex networks. The results obtained are applied on spring-mass-damper systems, demonstrating their effectiveness and it is expected that the proposed approach can be extended to more practical physical engineering systems.

This paper predominantly studies how to achieve the mean-square exponential stability (MSES) of stochastic highly nonlinear fuzzy systems with Markov jump and periodic time-varying delay (SHNFSMPTD), using asynchronous switching fuzzy control. Considering the time-varying delay and the drift and diffusion terms satisfying polynomial growth conditions, we construct two different functionals that explicitly depend on time t in the monotonically increasing and decreasing intervals, respectively. Combined with Dupire’s functional Itô formula, graph theory, and the properties of periodic time-varying delay, we can show that the negative definiteness of the functionals holds in both intervals, which leads to the stability of systems. In addition, by combining the generator matrix of Markov jump and the conditional probability matrix of asynchronous switching, we provide additional MSES criteria for SHNFSMPTD under asynchronous switching fuzzy control. Ultimately, the theoretical results obtained are utilized in a class of van der Pol-Duffing oscillators (VDPDO), and the six-robot systems with center pattern generator networks, and the feasibility of the theoretical results is illustrated through numerical simulations. Note to Practitioners—Stochastic highly nonlinear fuzzy systems with Markov jump and periodic time-varying delays are widely found in many practical systems, such as communication networks, control systems, and biological rhythm systems. In this paper, we propose for the first time to deal with the exponential stability problem of such systems using Dupire’s functional Itô formula. By constructing suitable functionals and applying Dupire’s functional Itô formula, we obtain the negative definiteness of the operator in both intervals. This paper provides a new method for the construction of Lyapunov functional and offers some new ideas for the stability study of this kind of systems. In the future, we attempt to study the noise stabilization of such systems with various attacks and intermittent communication under intermittent control.

This paper investigates the stabilization of highly nonlinear stochastic delayed large-scale networks (HSDLN) based on asynchronously delayed intermittent decentralized control (ADIDC). By incorporating highly nonlinearity into the networks, practical problems can be more accurately modeled, and the nonlinear coupling relationships among nodes can be effectively captured, vastly expanding the practical application scope. ADIDC effectively integrates the advantages of asynchronously intermittent decentralized control and delayed intermittent control, enabling the networks to achieve the desired behavior. Subsequently, we set up an auxiliary timer and then define a newfangled Lyapunov functional. In particular, an innovative Lyapunov-based analysis, not utilizing Halanay-type differential inequality, is introduced to obtain a stabilization criterion for HSDLN, which effectively copes with asynchronously intermittent decentralized control and highly nonlinear, stochastic, and delayed elements. Meanwhile, a graph-theoretic methodology is employed to address the cross-terms arising in an asynchronous sense. Ultimately, as a practical application of the theoretical findings, a class of FitzHugh-Nagumo models is considered, and the stabilization is validated through numerical simulations. Note to Practitioners—This paper is motivated by existing results on various intermittent controls for the dynamics of complex networks. The existing results mainly require intermittent controls to be continuously/discretely synchronous sampled-data each node of complex networks, which limits the application scope of intermittent controls. This paper designs a new hybrid control called asynchronously delayed intermittent decentralized control. Particularly, asynchronously intermittent sampled-data control is a special case of control in this paper. Moreover, some lower conservative sufficient conditions are derived, such as local Lipschitz condition and polynomial growth condition instead of global Lipschitz condition and linear growth condition for coefficients of complex networks, and the average work time ratio instead of the maximum rest time ratio for intermittent control. The proposed results provide a novel idea for the stabilization study of FitzHugh-Nagumo models, and it is expected that the proposed methods can be extended to more actual physical engineering systems.

This article focuses on stabilizing highly nonlinear hybrid stochastic complex dynamical networks with time delays (HSCNT) via sampled-data control with asynchronously periodic self-triggered intermittent decentralized strategy (SCAPI). Considering the constraints imposed by linear growth conditions in real models, we introduce high nonlinearity into the networks. Moreover, considering the possibility of nonsimultaneous transmission of control information by the controllers, the asynchronous decentralization is thus brought in periodic self-triggered intermittent control for the first instance. Then, to resolve the problems caused by asynchronous decentralization, a graph-theoretic approach is employed. Combining this with an auxiliary timer, an innovative Lyapunov functional is designed, after which an original Lyapunov-based method is proposed to cope with the complexity of introducing high nonlinearity and asynchronous decentralization into networks. In particular, some numerical simulations are provided for demonstration.

In the article, a stabilized issue for complex-valued hybrid stochastic multilinks networks (CHSMNs) is investigated under event-triggered control (E-TC). In contrast to existing literature, the proposed E-TC defines the event-triggered instant sequence as the random sequence rather than the number sequence, which is more accurate concerning hybrid stochastic systems. Especially, a modified more general event-triggered function is proposed. After the Zeno behavior is eliminated by the contradiction, several stabilized conditions are established to guarantee the input-to-state stability and exponential stability in the mean square and almost surely exponential stability of CHSMNs, where studying in the complex domain and no splitting real and imaginary parts. Subsequently, we analyze the lower bound of the event-triggered intervals for E-TC in the sense of mathematical expectation. Whereafter, the stabilized problem for the Cohen–Grossberg neural networks (CSDLCNs) and the islanded micro grid model (IMGM) is considered as an application. Meanwhile, numerical simulations are presented for verification.

In this paper, the semi-global exponential stability of semi-Markov jump systems with distributed delay under semi-global sampling control is studied. Besides, a new definition of functional derivative associated with the semi-Markov jump is given. By using the global exponential stability of semi-Markov jump system with distributed delay under global continuous control, incorporation with the inequality technique, the semi-global exponential stability criteria of semi-Markov jump system with distributed delay under semi-global sampling control are given, including Lyapunov-type theorem and coefficient-type theorem. Eventually, an application about a class of oscillator systems combining the theoretical results is discussed and the corresponding numerical example is presented to demonstrate the effectiveness of the theoretical results.Note to Practitioners—Sampling control has gained broad attention for its cost-saving and reliability. In some practical sampling control systems, due to the inner property, they can not achieve stability in global scope but only in local range and the converge speed depends on the initial value. In this paper, we give a novel definition of horizontal movement of the segment function and Dini’s derivate of the constructed functional is presented basically, which is adapted to more than the solution of the systems and is of much flexibility. The maximum sampling interval is provided to make the sampling control systems keep stable. And the results provide a reference for the semi-global stability of oscillator systems with semi-Markov jump under sampling control.

This paper investigates the T-S fuzzy-based bipartite quasi-synchronization of fractional-order heterogeneous coupled reaction-diffusion neural networks. In the considered neural networks, interactions between adjacent neurons are time-varying, cooperative, and competitive, and heterogeneity and T-S fuzzy system rule are simultaneously introduced to characterize the parameter uncertainty arising from complexity and ambiguity in the real world. A new time-varying graph-theoretic Lyapunov function is given for time-varying coupled reaction-diffusion neural networks. Meanwhile, a more general fractional-order derivative law is provided to estimate the derivative of this function, which includes the existing fractional-order derivative laws. Based on a fuzzy-based aperiodically intermittent control, some sufficient conditions are offered for the bipartite quasi-synchronization under a time-varying graph-theoretic Lyapunov function, and the allowable error bound is given. Finally, we carry out some simulations numerically to show the validity of the theory.

Numerous previous findings on the synchronization of fractional-order networks have been conducted through event-triggered control (ETC) or intermittent control (IC), separately. Motivated by the benefits of IC and ETC, this article designs an effective event-triggered intermittent control (ETIC) to investigate the bipartite synchronization of fractional-order fuzzy signed networks. The system dynamics are constructed to describe the nonlinear signed networks via the fuzzy logic and the short-memory performance. Notably, this article represents the first attempt to design the ETIC for fractional-order networks in the sense of exponential convergence. This approach avoids the constantly updating states of IC and the uninterrupted input of ETC. By employing the Lyapunov method, some sufficient conditions for the synchronization of the considered networks are obtained. In addition, the Zeno phenomenon is eliminated so that the infimum of interval length is positive, which ensures the feasibility of the designed controller. Finally, two numerical experiment examples of the fractional-order Chua's circuits model and the fractional-order power system without load disturbance are carried on to illustrate the effectiveness and practicability of our theoretical analysis.

This article investigates the problem of exponential bipartite synchronization of fractional-order multilayer signed networks via hybrid impulsive control. First, the mathematical model of the networks is established by integrating the fractional dynamics of nodes, the multilayer network edges, and the positive and negative weights (antagonistic relationship), which is more pluralistic and practical. Second, a hybrid impulsive controller is designed, which is composed of the feedback control part and the impulsive control part to realize the exponential bipartite synchronization objective. Both positive and negative impulsive effects are considered and the ranges of the impulsive control gain related to the order of Caputo fractional derivative are discussed. In addition, some sufficient conditions for exponential bipartite synchronization of fractional-order multilayer signed networks are obtained by using the signed graph theory, Lyapunov method, and average impulsive interval method. Furthermore, in order to illustrate the practicability of the theoretical results, fractional-order coupled Chua's circuits model and fractional-order power systems built on multilayer signed networks are established and the exponential bipartite synchronization issues are analyzed. Numerical examples and simulations are provided to show the effectiveness of the obtained results.

In this article, finite-time synchronization is investigated for fractional-order fuzzy time-varying coupled neural networks subject to reaction–diffusion by establishing a new framework under fuzzy-based feedback control and fuzzy-based adaptive control. For the considered networks, we put forward an innovative graph-theory-based time-varying Lyapunov function. To overcome the difficulty of estimating the fractional derivative of this function, this article proposes a novel fractional derivative rule. Through graph theory and the Lyapunov method, several finite-time synchronous criteria are obtained for the considered networks, and the estimation of the settling time is derived. Finally, the numerical results are shown to demonstrate the practicability of the given results.

This study proposes a novel dynamic event-triggered impulsive control (ETIC) scheme to study the exponential stabilization of general stochastic nonlinear systems, where the impulsive sequence is determined by a dynamic event-triggered mechanism. The dynamic ETIC can effectively reduce controller updates and significantly save energy under the same decay rate compared to traditional static event-triggered impulsive generators. Additionally, there is a guaranteed positive minimum inter-event time for each sample path solution of systems. Furthermore, the proposed dynamic ETIC scheme is employed to stabilize stochastic complex networks based on the graph theory and the Lyapunov method. Finally, we provide two illustrative examples to verify the effectiveness and correctness of the proposed dynamic ETIC scheme.

This article deals with the almost surely exponential synchronization issue for complex dynamical networks (CDNs) under noise control. Different from most of the existing literature, aperiodically intermittent discrete observations noise control is proposed. It is worth noting that the state in noise work time is discretely observed rather than continuously. Meanwhile, some sufficient conditions are presented based on stochastic analytical techniques and the Lyapunov method. Besides, the upper bounds of noise rest rate and the time lag between two consecutive observations are estimated. Moreover, it is clear that CDNs are easier to achieve the almost surely exponential synchronization when noise control gain becomes larger. To demonstrate the effectiveness and feasibility of analytical results, two applications about single-link robot arm systems as well as second-order oscillator systems are given. At the same time, some numerical simulations are exhibited.

This article discusses the exponential stability in mean square of Takagi–Sugeno fuzzy systems (T-SFSs) under the stochastic case. Moreover, stochastic factors are taken into account to make the model more general. Different from traditional time-triggered control, we introduce event-triggered control strategy into intermittent control and then intermittent dynamic event-triggered control (IDE-TC) is developed, which can reduce updates of the controller and save resources. Besides, we eliminate Zeno phenomena, which is independent of mathematical expectation. Furthermore, the minimum interexecution time by the IDE-TC can be obtained directly for T-SFSs under the stochastic case. In addition, in order to illustrate the theoretical results, an application about double-link robot arm model is given. Meanwhile, we exhibit some numerical simulations.

A new consensus protocol with aperiodically intermittent discrete-time state observation noise (AIDSON) is introduced. With the help of the proposed AIDSON, the almost sure exponential consensus (ASEC) of multiagent systems is investigated. Through the Lyapunov method and stochastic comparison principle, some sufficient conditions can be obtained. Moreover, the upper bounds of the rest rate of intermittent communication noise and the duration between two consecutive observations are estimated. Additionally, the larger the noise intensity is, the faster multiagent systems reach the ASEC. Furthermore, the established results are applied to the consensus analysis of single-link robot arms and oscillators and some simulations are presented.

A novel intermittent dynamic event-triggered control is proposed to investigate the exponential synchronization in mean square (ESMS) of stochastic complex networks (SCNs). In contrast to existing literature, the proposed intermittent control is based on dynamic event-triggering instead of static time-triggering during the control interval. Meanwhile, the number of event triggers can be reduced by introducing an exponential function. Moreover, for each sample path solution of SCNs, the existence of a minimum positive inter-event time is guaranteed in all the event-generators proposed in this paper. In addition, based on the Lyapunov method and the graph theory, synchronization criteria for the ESMS of SCNs under the intermittent dynamic event-triggered control are established. Finally, theoretical results are applied to islanded microgrid systems and simulations are given to verify the effectiveness of the results.

In this article, the exponential stability problem for fractional-order complex multi-links networks with aperiodically intermittent control is considered. Using the graph theory and Lyapunov method, two theorems, including a Lyapunov-type theorem and a coefficient-type theorem, are given to ensure the exponential stability of the underlying networks. The theoretical results show that the exponential convergence rate is dependent on the control gain and the order of fractional derivative. To be specific, the larger control gain, the higher the exponential convergence rate. Meanwhile, when aperiodically intermittent control degenerates into periodically intermittent control, a corollary is also provided to ensure the exponential stability of the underlying networks. Furthermore, to show the practicality of theoretical results, as an application, the exponential stability of fractional-order multi-links competitive neural networks with aperiodically intermittent control is investigated and a stability criterion is established. Finally, the effectiveness and feasibility of the theoretical results are demonstrated through a numerical example.

The pth moment exponential synchronization (PMES) problem for time-varying complex dynamical networks (CDNs) with multiple time-varying delays (TCDNMTDs) by aperiodically intermittent control is studied in this paper. Compared with related work, the coupling structure of CDNs is time varying. Also, internal time-varying delays and coupling time-varying delays are taken into consideration and they are different from each other. It is worth emphasizing that the intermittent control scheme proposed here is nonperiodical. Some criteria are derived to make TCDNMTDs achieve PMES by using the Lyapunov method and graph theory. Additionally, we also consider the synchronization of second-order Kuramoto oscillators and coupled Chua's circuits and some numerical simulations are presented to verify the validity of our results.

In this paper, to investigate the exponential synchronization of stochastic neural networks, a new periodically intermittent discrete observation control (PIDOC) is first proposed. Different from the existing periodically intermittent control, our control in control time is feedback control based on discrete-time state observations (FCDSOs) instead of a continuous-time one. By employing the Lyapunov method, graph theory, and theory of differential inclusions, the exponential synchronization of stochastic neural networks with a discontinuous right-hand side is realized by PIDOC and some sufficient conditions are presented. Especially, when control width tends to control period, PIDOC will be reduced to a general FCDSO and we give some detailed discussions. Then, we provide some corollaries about synchronization in mean square, asymptotical synchronization in mean square, and exponential synchronization of stochastic neural networks under FCDSO. Finally, some numerical simulations are provided to demonstrate our analytical results.

We introduce a class of novel stochastic coupled systems in which the coupling structure is time-varying and the topology structure is not strongly connected, and first establish the system on a digraph with a time-varying weight matrix. Motivated by Du and Li (2014), we give a hierarchical method to deal with digraphs without strong connectivity and establish the corresponding hierarchical algorithm to realize this approach. Also, an example is given to illustrate our hierarchical algorithm and its feasibility. In the sequel, based on the theory of asymptotically autonomous systems, Kirchhoff's matrix tree theorem, and Lyapunov method, several moment exponential stability criteria are presented, including a Lyapunov-type theorem and a coefficient-type criterion. Furthermore, theoretical results are applied to stochastic coupled oscillators with time-varying coupling structure (SCTCS), and the stability criterion of SCTCS is obtained. Finally, the effectiveness of theoretical results is illustrated by two numerical examples.