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In this work, the problem of passivity-based synchronization for coupled chaotic neural networks with randomly occurring time delays is addressed. The topology switching of the networks is subject to the semi-Markov process. Some Bernoulli random variables are used to simulate the randomly occurring phenomena of the aforesaid networks. Furthermore, the main objective is to develop the synchronization criteria such that the considered networks can achieve global stochastic synchronization and conform to the passive performance index. Subsequently, by using some relatively advantageous inequalities and reasonable matrix transformation techniques, some available synchronization criteria are derived. Ultimately, an example is presented to illustrate the applicability and availability of the method proposed. [ABSTRACT FROM AUTHOR]

This work investigates the dissipativity and stability analysis problems for Markov jump generalized neural networks subject to time-varying interval delays. The aim of the present study is to determine whether the new dissipativity and stability criteria with less conservatism could be established for Markov jump generalized delayed neural networks or not. In this connection, a more general dissipative property index inequality is firstly introduced. On basis of fully considering mode-dependent matrices in the Lyapunov–Krasovskii functional, some advantageous negative terms ignored in some existing works are taken into account. By employing some novel integral inequalities and stochastic analysis theory, some available less conservative criteria are developed. Three compared examples are finally shown to explain the reduced conservatism and superiority of the presented criteria for Markov jump generalized delayed neural networks. [ABSTRACT FROM AUTHOR]

Abstract For complex dynamic networks subject to switching topologies, an H ∞ event-triggered control scheme is developed to deal with the finite-time synchronization problem. A semi-Markov process is employed to govern the switching of the networks topologies. The purpose focuses on designing a controller via the event-triggered scheme, which guarantees that the resulting error networks are finite-time bounded with a prescribed level of the H ∞ performance. By utilizing the stochastic analysis theory and finite-time synchronization concept, some sufficient conditions are deduced to determine whether the desired controller will exist or not for the complex dynamic networks. Eventually, an illustrated example is proposed to explain the validity and practicability of this method. [ABSTRACT FROM AUTHOR]

Abstract In this work, a kind of switched gene regulatory networks with packet dropout and uncertainties are constructed by switched coupled nonlinear difference equations. In comparison, a more comprehensive switching regulation, persistent dwell-time, is employed to it. The aim is to construct a mixed mode-dependent and mode-independent estimator for the before-mentioned gene regulatory networks with a view to the loss of system modal information. Thereafter, the augmented system is established. After that, the sufficient conditions of the exponential stability and mixed H ∞ / l 2 − l ∞ performance for the augmented system are deduced by the switching Lyapunov theory. Finally, a numerical example is employed to elucidate the validity of the estimator gains decoupled by the congruent transformation. [ABSTRACT FROM AUTHOR]

This paper deals with stability analysis and control synthesis for positive semi-Markov jump systems (S-MJSs) with time-varying delay, in which the stochastic semi-Markov process related to nonexponential distribution is considered. The main motivation for this paper is that the positive condition sometimes needs to be considered in S-MJSs and the controller design methods in the existing have some conservation. To deal with these problems, the weak infinitesimal operator is firstly derived from the point of view of probability distribution under the constraint of positive condition. Then, some sufficient conditions for stochastic stability of positive S-MJSs are established by implying the linear Lyapunov–Krasovskii functional depending on the bound of time-varying delay. Furthermore, an improved stabilizing controller is designed via decomposing the controller gain matrix such that the resulting closed-loop system is positive and stochastically stable in standard linear programming. The advantages of the new framework lie in the following facts: (1) the weak infinitesimal operator is derived for S-MJSs with time-varying delay under the constraint of positive condition and (2) the less conservative stabilizing controller is designed to achieve the desired control performance. Finally, three examples, one of which is the virus mutation treatment model, are given to demonstrate the validity of the main results. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of reachable set estimation for a class of uncertain singular systems with time-varying delays from a new point of view. Our consideration is centered on the design of a proportional-derivative state feedback controller (PDSFC) such that the considered singular system is robustly normalizable and all the states of the closed-loop system can be contained by a bounded set under zero initial conditions. First, a nominal singular time-delay system is considered and sufficient conditions are obtained in terms of matrix inequalities for the existence of a PDSFC and an ellipsoid. In this case, the considered system is guaranteed to be normalizable and the reachable set of the closed-loop systems is contained by the ellipsoid. Then, the result is extended to the case of singular time-delay systems with polytopic uncertainties and relaxed conditions are derived by introducing some weighting matrix variables. Furthermore, based on the obtained results, the reachable set of the considered closed-loop singular system can be contained in a prescribed ellipsoid. Finally, the effectiveness of our results are demonstrated by two numerical examples. [ABSTRACT FROM AUTHOR]

This paper deals with the problem of controller design for time-delay system with stochastic disturbance and actuator saturation. By use of more appropriate Lyapunov–Krasovskii functional (LKF) and a new criterion for the domain of attraction, less conservative conditions for stochastic stability are proposed. Then, the difficulties of the domain of attraction confronted in system analysis and synthesis can be overcome. These sufficient conditions are derived in terms of linear matrix inequality (LMI). Finally, two practical examples demonstrate the validity of the given results. [ABSTRACT FROM AUTHOR]

• A novel distributed filtering compensation algorithm is presented in terms of the available transmitted data. • The expression form of minimized upper bound of filtering error covariance matrix and the desired filter gain are established. • The filtering algorithm performances are analyzed by providing the theoretical proofs regarding the boundedness. This paper investigates the distributed filtering (DF) issue for a class of time-varying state-saturated systems with packet disorders (PDs) via the event-triggered communication mechanism (ETCM). The random transmission delays, which can be characterized by a set of random variables obeying certain probability distribution, cause the phenomenon of PDs. In addition, for the sake of decreasing the consumption of network resources, the ETCM is used to arrange the data transmission. On the basis of the measurable data information, a novel distributed filter is constructed that can ensure the existence of the upper bound matrix (UBM) regarding the filtering error (FE) covariance and then the trace of the presented UBM is minimized via constructing the suitable filter gain. Afterwards, the boundedness analysis of FE dynamics is provided to evaluate the filtering algorithm performance. Finally, the validity of the designed DF scheme is illustrated through a numerical experiment. [ABSTRACT FROM AUTHOR]

H ∞ finite-time control for uncertain system with the unmeasurable state via the sliding mode control (SMC) approach is discussed in this article. Our attention is to design an appropriate finite-time SMC law to attenuate the influences of parametrical uncertainty and external disturbance. First, an appropriate non-fragile observer-based finite-time SMC law is designed such that the state trajectories can arrive at the specified sliding surface during the finite-time interval. Then, finite-time boundedness (FTBs) is well implemented by partitioning strategy and sufficient conditions are given to realize FTBs for the augment system with H ∞ performance. Next, the controller gain and observer gain are obtained by solving the corresponding linear matrix inequalities (LMIs). Finally, a RLC series circuit shows the effectiveness of the proposed SMC approach. [ABSTRACT FROM AUTHOR]

This paper investigates the issue of robust stabilization for delayed semi-Markov jump T-S fuzzy systems via sliding mode control (SMC). In order to reduce some conservativeness, an integral sliding mode surface (ISMS) is designed without assumption that the input matrices are plat-rule independent with full column rank, which is one of the critical factors for system performance. Based on Lyapunov functional theory, sufficient condition is provided for stochastic stability of the closed-loop system, and then extended to the case where the input matrices are independent of plant-rule. In addition, a fuzzy SMC controller is established to guarantee the finite time reachability of the predetermined fuzzy manifold. Finally, the superiorities of the proposed method are validated by a single-link robot arm model. [ABSTRACT FROM AUTHOR]

Exponential mean-square stability for delayed switched systems with Markov jump parameters and generally incomplete transition rates is discussed. The switching dynamics among the operation modes are considered to be governed by a high level with average dwell time switching (ADTS) and a low level with stochastic Markov switching. Many practical systems such as general economic model subject to unpredictable structural changes can be described by switching Markov jump systems (SMJSs) with generally incomplete transition rates. By resorting to average dwell time switching approach, sufficient conditions are proposed to ensure the underlying system exponentially mean-square stable. Finally, the theoretical results are applied to a general economic model to demonstrate the effectiveness, applicability and superiority of the main results. [ABSTRACT FROM AUTHOR]

This paper deals with the problem of disturbance-observer-based control (DOBC) for semi-Markovian jump systems (S-MJSs) with generally uncertain transition rate (TR) and saturation nonlinearity. Unlike the existing theories, the proposed method considers the external disturbance and saturation nonlinearity in S-MJSs with more general TR. First of all, to study this DOBC problem, the sufficient condition for stochastic stability of the system is derived by the use of Lyapunov–Krasovskii functional. Then, the design methods of the anti-disturbance controller and the disturbance observer are proposed based on the given stability condition of the closed-loop system. Furthermore, the maximum domain of attraction is estimated by solving an optimization iterative algorithm. Finally, two numerical examples are given to prove the correctness of the proposed results. [ABSTRACT FROM AUTHOR]