Robust impulsive synchronization of complex delayed dynamical networks

This Letter investigates robust impulsive synchronization of complex delayed dynamical networks with nonsymmetrical coupling from the view of dynamics and control. Based on impulsive control theory on delayed dynamical systems, some simple yet generic criteria for robust impulsive synchronization are established. It is shown that these criteria can provide a novel and effective control approach to synchronize an arbitrary given delayed dynamical network to a desired synchronization state. Comparing with existing results, the advantage of the control scheme is that synchronization state can be selected as a weighted average of all the states in the network for the purpose of practical control strategy. Finally, numerical simulations are given to demonstrate the effectiveness of the proposed control methodology.     

A Lie algebraic condition for exponential stability of discrete hybrid systems and application to hybrid synchronization

A Lie algebraic condition for global exponential stability of linear discrete switched impulsive systems is presented in this paper. By considering a Lie algebra generated by all subsystem matrices and impulsive matrices, when not all of these matrices are Schur stable, we derive new criteria for global exponential stability of linear discrete switched impulsive systems. Moreover, simple sufficient conditions in terms of Lie algebra are established for the synchronization of nonlinear discrete systems using a hybrid switching and impulsive control. As an application, discrete chaotic system's synchronization is investigated by the proposed method.     

Synchronization of impulsively coupled complex systems with delay

This paper investigates the synchronization of complex systems with delay that are impulsively coupled at discrete instants only. Based on the comparison theorem of impulsive differential system, a distributed impulsive control scheme is proposed to achieve the synchronization for systems with delay. In the control strategy, the influence of all nodes to network synchronization relies on its weight. The proposed control scheme is applied to the chaotic delayed Hopfield neural networks and numerical simulations are presented to demonstrate the effectiveness of the proposed scheme.     

Impulsive synchronization of chaotic Lur'e systems via partial states

In this Letter, the problem of impulsive synchronization of two identical Lur'e systems via partial states is studied. The problem arises in the situation when only partial states of the driven systems are available. By using the method of the variation of parameters for linear impulsive systems and some analysis technique, a sufficient condition for the existence of the impulsive control law for synchronization via partial states is derived. The sufficient condition is given in terms of linear matrix inequalities concerning the interconnection matrices. By using this result, we propose a new impulsive synchronization scheme for a class of Lur'e systems. The new impulsive synchronization scheme only exerts the impulsive input on partial states of the driven system and is characterized by a set of conditions related to the impulsive interval bound, the impulsive magnitude and a coupling condition between them. The proposed impulsive synchronization method is illustrated through Chua's circuit.     

Impulsive Synchronization of Laser Plasma System

The issue of impulsive synchronization of the coupled chaotic laser plasma system is investigated. A new framework for impulsive synchronization of such chaotic systems is presented, which makes the synchronization error system a linear impulsive control system. We derive some sufficient conditions for the synchronization of a laser plasma system via impulsive control with the varying impulsive intervals, which allows us to derive the impulsive synchronization law easily. To illustrate the effectiveness of the proposed results, two numerical examples are given.     

Cluster synchronization of community network with distributed time delays via impulsive control

Cluster synchronization is an important dynamical behavior in community networks and deserves further investigations.A community network with distributed time delays is investigated in this paper.For achieving cluster synchronization,an impulsive control scheme is introduced to design proper controllers and an adaptive strategy is adopted to make the impulsive controllers unified for different networks.Through taking advantage of the linear matrix inequality technique and constructing Lyapunov functions,some synchronization criteria with respect to the impulsive gains,instants,and system parameters without adaptive strategy are obtained and generalized to the adaptive case.Finally,numerical examples are presented to demonstrate the effectiveness of the theoretical results.     

Lag synchronization of chaotic systems with time-delayed linear terms via impulsive control

In this paper, the lag synchronization of chaotic systems with time-delayed linear terms via impulsive control is investigated. Based on the stability theory of impulsive delayed differential equations, some sufficient conditions are obtained guaranteeing the synchronized behaviours between two delayed chaotic systems. Numerical simulations on time-delayed Lorenz and hyperchaotic Chen systems are also carried out to show the effectiveness of the proposed scheme. Note that under the scheme the chaotic system is controlled only at discrete time instants, and so it reduces the control cost in real applications.     

Impulsive control of time-delay systems using delayed impulse and its application to impulsive master-slave synchronization

This Letter is concerned with impulsive control of a class of nonlinear time-delay systems. Some uniform stability criteria for the closed-loop time-delay system under delayed impulsive control are derived by using piecewise Lyapunov functions. Then the criteria are applied to impulsive master-slave synchronization of some secure communication systems with transmission delays and sample delays under delayed impulsive control. Two numerical examples are given to illustrate the effectiveness of the derived results.     

Synchronization in complex delayed dynamical networks with impulsive effects

The present paper is mainly concerned with the issues of synchronization dynamics of complex delayed dynamical networks with impulsive effects. A general model of complex delayed dynamical networks with impulsive effects is formulated, which can well describe practical architectures of more realistic complex networks related to impulsive effects. Based on impulsive stability theory on delayed dynamical systems, some simple but less conservative criterion are derived for global synchronization of such dynamical network. It is shown that synchronization of the networks is heavily dependent on impulsive effects of connecting configuration in the networks. Furthermore, the theoretical results are applied to a typical SF network composing of impulsive coupled chaotic delayed Hopfield neural network nodes, and are also illustrated by numerical simulations.     

Global impulsive exponential synchronization of stochastic perturbed chaotic delayed neural networks

In this paper, the global impulsive exponential synchronization problem of a class of chaotic delayed neural networks (DNNs) with stochastic perturbation is studied. Based on the Lyapunov stability theory, stochastic analysis approach and an efficient impulsive delay differential inequality, some new exponential synchronization criteria expressed in the form of the linear matrix inequality (LMI) are derived. The designed impulsive controller not only can globally exponentially stabilize the error dynamics in mean square, but also can control the exponential synchronization rate. Furthermore, to estimate the stable region of the synchronization error dynamics, a novel optimization control algorithm is proposed, which can deal with the minimum problem with two nonlinear terms coexisting in LMIs effectively. Simulation results finally demonstrate the effectiveness of the proposed method.     

Robust lag synchronization between two different chaotic systems via dual-stage impulsive control

In this paper, an improved impulsive lag synchronization scheme for different chaotic systems with parametric uncertainties is proposed. Based on the new definition of synchronization with error bound and a novel impulsive control scheme (the so-called dual-stage impulsive control), some new and less conservative sufficient conditions are established to guarantee that the error dynamics can converge to a predetermined level, which is more reasonable and rigorous than the existing results. In particular, some simpler and more convenient conditions are derived by taking the same impulsive distances and control gains. Finally, some numerical simulations for the Lorenz system and the Chen system are given to demonstrate the effectiveness and feasibility of the proposed method.     

Impulsive stabilization and synchronization of a class of chaotic delay systems

The problems of control and synchronization of a class of chaotic systems with time delay via the impulsive control approach are investigated. Based on the Lyapunov-like stability theory for impulsive functional differential equations, several sufficient conditions are derived to guarantee chaos control and synchronization. Furthermore, we address the chaos quasisynchronization in the presence of single-parameter mismatch. Several illustrated examples are also given to show the effectiveness of the proposed methods.     

Controlling chaotic Lu systems using impulsive control

This Letter derives some sufficient conditions for the stabilization and synchronization of Lu systems via impulsive control with varying impulsive intervals and the more general quadratic Lyapunov function.     

Impulsive synchronization of two coupled complex networks with time-delayed dynamical nodes

In this paper, we investigate the impulsive synchronization between two coupled complex networks with time-delayed dynamical nodes. Based on the Lyapunov stability, the linear feedback control and the impulsive control theories, the linear feedback and the impulsive controllers are designed separately. By using the generalized Barbalat's lemma, the global asymptotic impulsive synchronization of the drive—response complex networks is derived and some corresponding sufficient conditions are also obtained. Numerical examples are presented to verify the effectiveness and the correctness of the synchronization criteria.     

Impulsive Synchronization of Lü Chaotic System Based on Small Impulsive Signal

In this Letter the issue of impulsive synchronization of the Lü chaotic system is developed. We propose an impulsive synchronization scheme of the Lü chaotic system including chaotic systems. Some new and sufficient conditions on varying impulsive distance are established in order to guarantee the synchronizability of the systems using the synchronization method. In particular, some simple conditions are derived in synchronizing the systems by equal impulsive distances. The proposed impulsive synchronization scheme is applied to the Lü chaotic system and the numerical example demonstrates the effectiveness of the method. The boundaries of the stable regions are also estimated.     

Impulsive synchronization of complex networks with non-delayed and delayed coupling

This Letter investigates the impulsive synchronization between two complex networks with non-delayed and delayed coupling. Based on the stability analysis of impulsive differential equation, the criteria for the synchronization is derived, and a linear impulsive controller and the simple updated laws are designed. Particularly, the weight configuration matrix is not necessarily symmetric or irreducible, and the inner coupling matrix need not be symmetric. Numerical examples are presented to verify the effectiveness and correctness of the synchronization criteria.     

Adaptive Impulsive Outer Synchronization Between Drive-Response Dynamical Networks

In this paper, outer synchronization between drive-response dynamical networks is investigated. Impulsive control combining with adaptive strategy is adopted to design controllers for achieving the goal. Based on the Lyapunov function method and mathematical analysis technique, a synchronization criterion with respect to the impulsive gains and intervals is analytically derived. From the criterion, the impulsive gains can adjust themselves to proper values when the impulsive intervals and some constants are fixed, and vice versa. Finally, two numerical examples are provided to verify the effectiveness of the derived result.     

Projective synchronization of a class of delayed chaotic systems via impulsive control

The Letter studies the projective synchronization of a class of delayed chaotic systems. The drive-response system can be synchronized to within a desired scaling factor via impulsive control. Some sufficient conditions are derived by the stability analysis of the impulsive functional differential equations. An illustrative example is provided to show the effectiveness and feasibility of the proposed method and results.     

Impulsive synchronization of networked nonlinear dynamical systems

In this Letter, we investigate the problem of impulsive synchronization of networked multi-agent systems, where each agent can be modeled as an identical nonlinear dynamical system. Firstly, an impulsive control protocol is designed for network with fixed topology based on the local information of agents. Then sufficient conditions are given to guarantee the synchronization of the networked nonlinear dynamical system by using algebraic graph theory and impulsive control theory. Furthermore, how to select the discrete instants and impulsive constants is discussed. The case that the topologies of the networks are switching is also considered. Numerical simulations show the effectiveness of our theoretical results.     

忆阻混沌系统的脉冲同步与初值影响研究

以光滑三次型磁控忆阻器的蔡氏电路为例, 研究了两个同构忆阻混沌系统的脉冲控制同步方法.基于Lyapunov稳定性理论, 给出了忆阻混沌系统的脉冲同步渐近稳定条件; 结合误差系统的最大条件Lyapunov指数谱, 讨论了系统初值对脉冲同步性能的影响, 并进行了相应的数值仿真实验.结果表明, 在合适的脉冲控制参数条件下, 同构的忆阻混沌系统的脉冲同步是可行而有效的; 忆阻混沌系统的初值对脉冲同步性能存在一定的影响, 但可通过增大脉冲耦合强度来抑制系统初值的影响.