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This paper focuses on event‐triggered sampled‐data synchronization of uncertain complex networks with time‐varying coupled delays. First of all, a discrete event‐triggered sampled‐data control scheme is adopted, which not only makes the state of the system be monitored in discrete time, but also the sampling information is effectively transmitted. The proposed event‐triggered mechanism effectively prevents Zeno behavior. In addition, we also use some novel piecewise time‐dependent Lyapunov–Krasovskii and Wirtinger inequality to handle the time‐varying delays and parameter uncertainties of complex networks. Then, synchronization criteria are given for uncertain complex networks. Finally, the simulation results show that the control scheme can significantly reduce the number of transmitted signals while maintaining the uncertain complex networks synchronization. [ABSTRACT FROM AUTHOR]

This paper studies the sliding mode control method for coupled delayed fractional reaction-diffusion Cohen–Grossberg neural networks on a directed non-strongly connected topology. A novel fractional integral sliding mode surface and the corresponding control law are designed to realize global Mittag-Leffler synchronization. The sufficient conditions for synchronization and reachability of the sliding mode surface are derived via the hierarchical method and the Lyapunov method. Finally, simulations are provided to verify our theoretical findings. [ABSTRACT FROM AUTHOR]

Summary: In this paper, we investigate the pinning synchronization of directed complex network with time‐varying delay under the adaptive aperiodically intermittent control. First, the model of a directed complex network is established, the interaction graph of which is not required to contain a directed spanning tree, and for which an adaptive aperiodically intermittent feedback controller is well designed. In addition, based on the Lyapunov function method and linear matrix inequality technique, several asymptotical synchronization criteria are derived via an aperiodically intermittent strategy, which is superior to the periodical scheme. Moreover, the adaptive strategy providing the exponential convergence rate and the pinning algorithm demonstrating how to select pinned nodes are presented. Finally, numerical examples are provided to illustrate the effectiveness of the derived theoretical results. [ABSTRACT FROM AUTHOR]

This paper mainly investigates two kinds of sliding mode synchronization (SMS) for multiple chaotic systems with unknown parameters and disturbances. Both multiple coupled systems and uncoupled systems are considered. For multiple uncoupled chaotic systems (MUCSs), the sliding mode control scheme is designed to ensure that multiple response systems synchronize with one drive system under the effects of external disturbances, and the appropriate adaptive laws are proposed to estimate unknown parameters. For multiple coupled chaotic systems (MCCSs), the definition of transmission synchronization is given first. Furthermore, a special integral sliding surfaces is selected, and the corresponding controllers with the compensation terms are developed to realize SMS between every drive chaotic system and every respond system in transmission mode. Finally, some numerical examples are presented to illustrate the validity of theoretical results. [ABSTRACT FROM AUTHOR]

This paper investigates two classes of synchronization problems of multiple chaotic systems with unknown uncertainties and disturbances by employing sliding mode control. Modified projective synchronization and transmission synchronization are discussed here. For the modified projective synchronization problem, sliding mode controllers are designed to ensure that multiple response systems synchronize with one drive system under the effects of external disturbances. For the transmission synchronization problem, based on adaptive sliding mode control, an integral sliding surface is selected and the adaptive laws are derived to tackle unknown uncertainties and disturbances for such systems. A class of nonlinear adaptive sliding mode controllers is developed to guarantee asymptotical stability of the error systems so that all chaotic systems can synchronize with each other. Simulation results are given to illustrate the effectiveness of the proposed schemes by comparing with the existing methods. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the hybrid synchronization behavior in an array of coupled chaotic systems with ring connection, of which means complete synchronization (CS) and anti-synchronization (AS) could coexist. First, the anti-synchronization controllers are designed, which can transform the synchronization error dynamic system into a nonlinear system with an antisymmetric structure. Second, we investigate the complete synchronization behavior in such a chaotic system under the anti-synchronization control. After that, the stability conditions are given for reaching hybrid synchronization. Finally, numerical examples and simulation results are presented to verify and validate the hybrid synchronization behavior in coupled chaotic system. [ABSTRACT FROM AUTHOR]

This paper addresses the exponential synchronization problem of a class of master-slave distributed parameter systems (DPSs) with spatially variable coefficients and spatiotemporally variable nonlinear perturbation, modeled by a couple of semilinear parabolic partial differential equations (PDEs). With a locally Lipschitz constraint, the perturbation is a continuous function of time, space, and system state. Firstly, a sufficient condition for the robust exponential synchronization of the unforced semilinear master-slave PDE systems is investigated for all admissible nonlinear perturbations. Secondly, a robust distributed proportional-spatial derivative (P-sD) state feedback controller is desired such that the closed-loop master-slave PDE systems achieve exponential synchronization. Using Lyapunov’s direct method and the technique of integration by parts, the main results of this paper are presented in terms of spatial differential linear matrix inequalities (SDLMIs). Finally, two numerical examples are provided to show the effectiveness of the proposed methods applied to the robust exponential synchronization problem of master-slave PDE systems with nonlinear perturbation. [ABSTRACT FROM AUTHOR]

This paper considers the synchronization and anti-synchronization problem of N different coupled chaotic systems with ring connections. Employing the direct design method to design the synchronization and anti-synchronization controllers which can transform the error systems into a stable system with special anti-symmetric structure. Some simple stability criteria are then derived for reaching the synchronization in such systems. It is proved that these criteria not only are easily verified, but also improve and generalize previously known results. Finally, numerical examples are provided to demonstrate the effectiveness of the theoretical. [ABSTRACT FROM AUTHOR]

In this paper, the synchronization problem of inertial neural networks with time-varying delays and generally Markovian jumping is investigated. The second order differential equations are transformed into the first-order differential equations by utilizing the variable transformation method. The Markovian process in the systems is uncertain or partially known due to the delay of data transmission channel or the loss of data information, which is more general and practicable to consider generally Markovian jumping inertial neural networks. The synchronization criteria can be obtained by using the delay-dependent Lyapunov–Krasovskii functionals and higher order polynomial based relaxed inequality (HOPRII). In addition, the desired controllers are obtained by solving a set of linear matrix inequalities. Finally, the numerical examples are provided to demonstrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

This paper investigates the synchronization control issue for a set of switched inertial neural networks in the discrete-time domain, in which the persistent dwell-time switching law is employed to depict the switchings among system parameters. Thereinto, the foregoing networks having the second-order differential equations are degraded to the first-order differential ones through applying the variable transformation. In addition, in order to cope with random gain fluctuations caused by noise or harsh environments, in the controller, two random variables obeying the Bernoulli distribution are employed to simulate the occurrence of gain fluctuations. Based on Lyapunov stability theory, persistent dwell-time concept and stochastic analysis theory, some sufficient criteria are derived under which the synchronization error system is exponentially mean-square stable with a prescribed l 2 - l ∞ property. Finally, a numerical example, including some illustrative simulations, is given to present the feasibility of the derived analytical results. [ABSTRACT FROM AUTHOR]

• The stochastic complex networks model with internal and coupled delays is established. • The pinning impulsive controller without sign function is designed to achieve finite-time synchronization. • A unified finite-time synchronization criterion is derived under synchronizing impulses and desynchronizing impulses. • The pinned nodes are related to the error values of the nodes, which improves the utilization of control resources. This paper mainly considers the finite-time synchronization (FTS) of stochastic complex networks with mixed delays via pinning impulsive control. Firstly, a novel pinning impulsive controller is introduced by selecting the nodes of the stochastic complex network with large error norms, which not only saves control resources, but also ensures that stochastic complex network with mixed delays can realize FTS. It is worth noting that the finite-time control strategy constructed is not affected by the sign function. Secondly, a uniform FTS criterion under synchronizing impulses and desynchronizing impulses is derived based on the idea of average impulsive interval. Moreover, the obtained sufficient condition are further extended to general stochastic complex networks and stochastic complex networks with mixed delays under delayed impulses. Finally, the feasibility of the theory results is verified by a numerical example. [ABSTRACT FROM AUTHOR]

• A novel Lyapunov–Krasovskii functional with a looped-functional is constructed % t k + 1 . • A more general inequality is utilized to process the integral with a derivative of the state variable. • An % H ∞ performance index is raised to deal with the control problem for sMJCDNs. This paper investigates the H ∞ exponential synchronization problem of delayed semi-Markov jump complex dynamical networks by utilizing the sampled-data control scheme. Through introducing a semi-Markov jump model, where the transition rate is related to the sojourn time, the addressed issue is therefore more general. By constructing a suitable Lyapunov–Krasovskii functional with a looped-functional and adopting an advanced inequality method, sufficient conditions for the H ∞ exponential synchronization of delayed semi-Markov jump complex dynamical networks are presented. A numerical example is finally employed to confirm the validity of the proposed method. [ABSTRACT FROM AUTHOR]