This paper investigates the exponential synchronization of nonidentically coupled Lur'e dynamical networks with proportional delay. Since the heterogeneities existed in different Lur'e systems, quasi-synchronization rather than complete synchronization is thus discussed. Different from general time delay, the proportional delay is a type of unbounded time-varying delay, which tremendously increases the requirements on network synchronization. Based on distributed impulsive pinning control protocol and different roles that impulsive effects play, the criteria for quasi-synchronization of nonidentically coupled Lur'e dynamical networks are derived by jointly applying the delayed impulsive comparison principle, the extended formula for the variation of parameters, and the definition of an average impulsive interval. Moreover, synchronization errors for different impulsive effects with different functions are evaluated and simultaneously, the corresponding exponential convergence rates are obtained. In addition, three numerical examples are presented to illustrate the validity of the control scheme and the theoretical analysis.

This paper is devoted to discuss the exponential synchronization for a kind of delay derivative coupled neural networks with stochastic disturbance and multiple time-varying delays. To simulate more practical situations and widen the synchronization applications in network science, the coupled neural networks with cluster-tree topology structure is studied by applying an impulsive pinning control strategy, which skillfully considered the neural networks in current cluster that directly linked to the neural networks in other clusters. Since the existence of delayed impulses, the general comparison principle for normal impulsive differential equations is efficiently extended. In view of the concept of average impulsive interval, the parameters classification discussion method and the mathematical induction method, some judgement conditions for achievement of the cluster synchronization on derivative coupled neural networks are derived. Additionally, the exponential convergence velocity of the derivative coupled neural networks is accurately estimated. Finally, numerical examples are presented to demonstrate the effectiveness of the control strategy and the theoretical results.

This paper is devoted to investigating the exponential synchronization problem on a class of coupled heterogeneous neural networks with hybrid time-varying delays. Since the heterogeneity of neural networks, the quasi-synchronization rather than complete synchronization is studied. Consider that the controller would suffer from impulsive disturbances, the distributed pinning control strategy is introduced. By jointly applying the concept of average impulsive intervals, the extended comparison principle of impulsive systems, and the vector norm techniques, sufficient conditions for the achievement of exponential quasi-synchronization on coupled heterogeneous neural networks are eventually obtained. In view that different impulsive effects play different roles in network synchronizing, two different situations of exponential synchronization are considered, respectively, by separately discussing the impulsive-effects-related parameter. Additionally, on account of the extended parameter variation formula for impulsive systems with hybrid time-varying delays, the exponential convergence velocities and the quasi-synchronization errors are estimated, separately, with respect to different ranges of impulsive effects. At last, three numerical examples with distinct impulsive effect values are given to illustrate the effectiveness of the theoretical analysis and the control schemes.

This paper investigates a self-triggered control scheme for a class of cyber-physical complex networks under deception attacks. The false data generated by attacks in both sensor-to-controller channels and controller-to-actuator channels are assumed to obey the Bernoulli distribution. By jointly combining distributed impulsive control scheme, time-varying impulsive effects and self-triggered strategy, a novel distributed self-triggered impulsive controller is elaborately designed. By integrating the definition of average impulsive gain, the contradiction analysis and Lyapunov stability theorem, sufficient conditions are derived for ensuring the secure synchronization within a given error bound. In addition, for further decreasing the triggering frequency and energy consumption, the advanced dynamic self-triggered criteria are obtained. It is worth mentioning that the updating laws adopted for dynamic self-triggered protocol in this paper is non-monotonic, which benefits to deal with the bounded synchronization. Finally, two numerical simulations are given to illustrate the feasibility of derived results.

Synchronization of complex networks with nonlinear couplings and distributed time-varying delays is investigated in this article. Since the mismatched parameters of individual systems, a kind of leader-following quasisynchronization issues is analyzed via impulsive control. To acquire appropriate impulsive intervals, the dynamic self-triggered impulsive controller is devoted to predicting the available instants of impulsive inputs. The proposed controller ensures the control effects while reducing the control costs. In addition, the updating laws of the dynamic parameter is settled in consideration of error bounds to adapt to the quasisynchronization. With the utilization of the Lyapunov stability theorem, comparison method, and the definition of average impulsive interval, sufficient conditions for realizing the synchronization within a specific bound are derived. Moreover, with the definition of average impulsive gain, the parameter variation scheme is extended from the fixed impulsive effects case to the time-varying impulsive effects case. Finally, three numerical examples are given to show the effectiveness and the superiority of proposed mathematical deduction.