In this paper, the problem of sliding mode control (SMC) is considered for a class of nonlinear continuous-time Markov jump systems (MJSs) with uncertainties and time delay. A novel integral-type switching sliding surface function is designed, where the controller gain may jump asynchronously with original MJSs. Then, an SMC law is constructed to force system trajectories onto the specified switching sliding surface in a finite time. The stochastic stability and dissipative performance of sliding mode dynamics are analyzed and the delay-dependent sufficient condition for the existence of the desired switching surface is developed. Moreover, we also extend SMC to investigate the finite-time stability problem during both reaching phase and sliding motion phase in the stochastic setting. Finally, simulation results are given to illustrate the effectiveness of the proposed design techniques.

This paper includes some results of switched Boolean control networks. The switched signals considered in this paper is time variant and it follows a certain probabilistic distribution vector. Given a concept of stabilization with stochastic switched signals, we obtained a necessary and sufficient condition for stabilization. Then a state feedback control depending on switched signals is designed to stabilize the system considered. Later we investigate a case when the switched signal θ(t) is unknown at time t, and what we have is the prediction switched signal ∧θ(t). For a given prediction matrix, a necessary and sufficient condition is given to preserve the stabilization. Except state feedback control, asynchronous pinning control for switched Boolean networks (BNs) is also considered. A necessary and sufficient condition is extended for the stability of BNs with stochastic switched signals. Moreover, algorithms are presented to find the minimal number of pinned nodes based on controlling minimal number of subsystems. Examples are shown to illustrate the effectiveness of the obtained results.

In Markov jump systems (MJSs), it is really difficult for the controller to perfectly follow the plant's mode transitions due to a number of practical factors. Therefore, this article considers to develop an asynchronous controller for a class of two-dimensional continuous-time MJSs. The relation of the plant's mode and the controller's mode is modeled by the hidden Markov model, i.e., the plant's mode influences the controller's transitions in a conditional probabilistic style. By defining a vector Lyapunov function, a sufficient condition for mean-square exponential stability and (U,R,S)- ε dissipativity is derived, whose feasible solutions give birth to a desired asynchronous controller. Finally, the influence of conditional probabilities on dissipativity performance is further studied through simulations.

This paper studies the event-triggered containment control (CC) problem of multiagent systems with a directed graph, where the followers' communication graph is an undirected graph. A novel event-triggered CC protocol is presented to schedule communications between agents, which depends on both local states and control inputs. Different from traditional approaches using broadcasts, a unique property of the proposed protocol is that it enables agent-to-agent data transmission. To do so, each communication link is associated with a specific local event. The estimated relative interagent states are transmitted over a specific link only when the related input-based event is detected. We develop sufficient conditions to solve CC problem under this protocol and extend it to the adaptive event-triggered protocol that does not require the global knowledge on the smallest positive eigenvalue of the Laplacian. For both protocols, we derive positive low bounds on the interevent time intervals generated by individual events, which eliminate the “Zeno phenomenon.” Feasibility of the proposed algorithm is verified by an example.

This paper investigates the problem of dissipativity-based asynchronous fuzzy integral sliding mode control (AFISMC) for nonlinear Markov jump systems represented by Takagi-Sugeno (T-S) models, which are subject to external noise and matched uncertainties. Since modes of original systems cannot be directly obtained, the hidden Markov model is employed to detect mode information. With the detected mode and the parallel distributed compensation approach, a suitable fuzzy integral sliding surface is devised. Then using Lyapunov function, a sufficient condition for the existence of sliding mode controller gains is developed, which can also ensure the stochastic stability of the sliding mode dynamics with a satisfactory dissipative performance. An AFISMC law is proposed to drive system trajectories into the predetermined sliding mode boundary layer in finite time. For the case with unknown bound of uncertainties, an adaptive AFISMC law is developed as well. The studied T-S fuzzy Markov jump systems involve both continuous-time and discrete-time domains. Finally, some simulation results are presented to demonstrate the applicability and effectiveness of the proposed approaches.

In this paper, the problem of asynchronous output feedback control is investigated for a class of Takagi-Sugeno fuzzy switched systems subject to intermittent measurements. The Bernoulli process is employed to model the phenomenon of stochastic intermittent measurements. Based on the hidden Markov model and output measurements, an asynchronous controller is designed. Then, sufficient conditions for the existence of an asynchronous controller are proposed, which ensure the stochastic stability of the closed-loop system with desired extended dissipative performance. Finally, an example is presented to illustrate the effectiveness and advantages of the proposed new design techniques.

In this paper, the stabilization problem of the Boolean network (BN) with stochastic disturbances via pinning control has been investigated. The necessary and sufficient conditions are given for robust stabilization of a BN with stochastic disturbances. Then, pinning control is considered to stabilize a BN with stochastic disturbances. An algorithm is given to obtain a new stable system and the pinning control, including the pinned nodes, control design, and control adding, is also solved. Finding the minimal number of pinned nodes is further analyzed. The necessary and sufficient conditions are obtained for the solvability of pinning control, based on which some matrices sets are constructed which leads to the necessary and sufficient conditions of pinning t nodes. Furthermore, an algorithm is introduced to search the minimal number of pinned nodes and what exactly they are, which will reduce the computational burden. Examples are given to illustrate the efficiency of the obtained results.

This paper studies the problem of event-triggered secure consensus for multiagent systems subject to periodic energy-limited denial-of-service (DoS) attacks, where DoS attacks usually prevent agent-to-agent data transmission. The DoS attacks are assumed to occur periodically based on the time-sequence way and the period of DoS attacks and the uniform lower bound of the communication areas are predetected by some devices. Based on the above assumptions, an event-based protocol consisting of two different measurements corresponding to leader-followers and follower-follower is presented to schedule communications between agents, which can reduce the update frequency of the controller. Then, the stability of the resultant error system is analyzed to derive sufficient conditions of achieving secure consensus by employing the Lyapunov function and the inductive approach. Besides, positive low bounds on any two consecutive intervals of events generated by individual events are calculated to eliminate "Zeno behavior" under the developed triggering condition and event-triggered protocol. Simulation result is provided to verify the theoretical analysis.

This paper applies an input-based triggering approach to investigate the secure consensus problem in multiagent systems under denial-of-service (DoS) attacks. The DoS attacks are based on the time-sequence fashion and occur aperiodically in an unknown attack strategy, which can usually damage the control channels executed by an intelligent adversary. A novel event-triggered control scheme on the basis of the relative interagent state is developed under the DoS attacks, by designing a link-based estimator to estimate the relative interagent state between intermitted communication instead of the absolute state. Compared with most of the existing work on the design of the triggering condition related to the state measurement error, the proposed triggering condition is designed based on the control input signal from the view of privacy protection, which can avoid continuous sampling for every agent. Besides, the attack frequency and attack duration of DoS attacks are analyzed and the secure consensus is reachable provided that the attack frequency and attack duration satisfy some certain conditions under the proposed control algorithm. “Zeno phenomenon” does not exhibit by proving that there exist different positive lower bounds corresponding to different link-based triggering conditions. Finally, the effectiveness of the proposed algorithm is verified by a numerical example.

A new globally exponentially synchronization criterion for complex dynamical networks is proposed in this paper taking account of discrete time communications units and time delay is considered, in which globally exponential convergence is achieved. By introducing larger decision matrices to gain time-delay synchronization criterion, it not only inherits the benefits of full utilization of available information, but also has less conservatism. At the same time, except for original system parameters, no more new decision variables are increased. A time-dependent Lyapunov functional approach is proposed to prove the effectiveness of the criterion. Some simulation results hold the feasibility of the theory.