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This study is concerned with the exponential $$H_{\infty }$$ synchronization criteria for complex dynamical networks of Lur'e- type systems with non-delay and delay couplings as well as external disturbances. The pinning sampled-data control is designed to achieve synchronization, in which only the selection of nodes is controlled, instead of the whole network. By constructing an improved Lyapunov-Krasovskii functional and utilizing the reciprocal convex method, the sufficient conditions are expressed in terms of linear matrix inequalities to ensure synchronization of the proposed network with a guaranteed $$H_{\infty }$$ performance. Different from most existing studies, the addressed synchronization criteria depend not only on the upper bounds of the sampling intervals but also on the lower bounds; therefore, potentially leading to reduced conservative criteria. The desired control gain matrices are calculated by solving the obtained linear matrix inequalities that guarantee the exponential stability of the error system under the $$H_{\infty }$$ norm. Finally, the effectiveness of the proposed method is demonstrated through numerical simulations. [ABSTRACT FROM AUTHOR]

This paper deals with the problem of robust $$H_{\infty }$$ synchronization of chaotic Lur'e systems with time-varying delays via sampled-data control. In order to make full use of the information about sampling intervals, nonlinear functions and time-varying delays, an improved Lyapunov-Krasovskii (L-K) functional is introduced. Based on reciprocal convex combination technique, sufficient conditions are derived in terms of linear matrix inequalities (LMIs) to ensure the asymptotic synchronization of the considered Lur'e system with a guaranteed $$H_{\infty }$$ performance. By solving the obtained LMIs, the required sampled-data control gain matrix is obtained, which assures the asymptotic stability of the error system and reduces the effect of external disturbance according to $$H_{\infty }$$ norm. Finally, the effectiveness and less conservatism of the proposed method are verified through numerical simulations of the Chua's circuit and neural networks. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of synchronization of identical and nonidentical memristor-based chaotic systems via active backstepping control technique. In order to achieve synchronization for identical chaotic systems, a memristor-based Lorenz system is considered as both master and slave systems, and for nonidentical chaotic systems, memristor-based Lorenz and Chuas systems are considered as master and slave systems, respectively. Based on the Lyapunov stability theory and active backstepping control technique, proper controllers are designed to achieve synchronization. Finally, numerical simulations are provided to show the effectiveness of the proposed controller. [ABSTRACT FROM AUTHOR]

In this paper, we address the problem of exponential synchronization of Markovian jumping complex dynamical networks with mode-dependent time-varying coupling delay via a stochastic sampled-data controller. In addition, the sampling period is assumed to be time-varying and switches between $$m$$ different values in a random way with given probability. By constructing a new Lyapunov-Krasovskii functional (LKF) with triple integral terms and by employing convex combination technique and free weighting matrices method, sufficient conditions for the coupled complex dynamical network to be globally exponentially synchronized in the mean square sense are derived. The information about the lower bound of the discrete time-varying delay is used in the LKF. Based on the derived condition, the desired sampled-data feedback controller is designed in terms of the solution to linear matrix inequalities. Finally, two numerical examples are given to illustrate the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

This paper investigates the delay-probability-distribution-dependent stability problem of uncertain stochastic genetic regulatory networks (SGRNs) with time-varying delays. The information of the probability distribution of the time-delay is considered and transformed into parameter matrices of the transferred SGRNs model. Based on the Lyapunov-Krasovskii functional and a stochastic analysis approach, a delay-probability-distribution-dependent sufficient condition is obtained in the linear matrix inequality (LMI) form such that delayed SGRNs are robustly globally asymptotically stable in the mean square for all admissible uncertainties. Three numerical examples are given to illustrate the effectiveness of our theoretical results. [ABSTRACT FROM AUTHOR]

Fuzzy cellular neural network (FCNN) structures are based on the uncertainties in human cognitive processes and in modeling neural systems, and they provide an interface between a human expert and classical cellular neural networks (CNNs). In this paper, an existence and global asymptotic stability analysis of the equilibrium point of FCNNs with time delay in the leakage term and unbounded distributed delays is investigated. Based on the Lyapunov-Krasovskii functional with free-weighting matrix, and using the homeomorphism mapping principle and linear matrix inequalities (LMIs), a new set of stability criteria for FCNNs is obtained with time delay in the leakage term, time-varying delays and unbounded distributed delays. The proposed results can be easily checked via the LMI Control Toolbox in MATLAB. Moreover, it is well known that the stability behavior of FCNNs is very sensitive to the time delay in the leakage term. In the absence of the leakage term, a new stability criterion is also derived by employing a Lyapunov-Krasovskii functional using an LMI approach. Numerical examples are provided to illustrate the effectiveness and reduced conservativeness of the developed techniques. [ABSTRACT FROM AUTHOR]