Jiang-Wen Xiao

Impulsive control for synchronization of a class of continuous systems

An impulsive control theory for synchronization of a class of continuous systems is developed. A sufficient condition for the impulsive control is derived. The proposed impulsive control scheme is illustrated by some continuous chaotic systems and the simulation results demonstrate the effectiveness of the method.

Global Synchronization of Complex Dynamical Networks Through Digital Communication With Limited Data Rate

This paper studies the global synchronization of complex dynamical network (CDN) under digital communication with limited bandwidth. To realize the digital communication, the so-called uniform-quantizer-sets are introduced to quantize the states of nodes, which are then encoded and decoded by newly designed encoders and decoders. To meet the requirement of the bandwidth constraint, a scaling function is utilized to guarantee the quantizers having bounded inputs and thus achieving bounded real-time quantization levels. Moreover, a new type of vector norm is introduced to simplify the expression of the bandwidth limit. Through mathematical induction, a sufficient condition is derived to ensure global synchronization of the CDNs. The lower bound on the sum of the real-time quantization levels is analyzed for different cases. Optimization method is employed to relax the requirements on the network topology and to determine the minimum of such lower bound for each case, respectively. Simulation examples are also presented to illustrate the established results.

Synchronization of Continuous Dynamical Networks With Discrete-Time Communications

In this paper, synchronization of continuous dynamical networks with discrete-time communications is studied. Though the dynamical behavior of each node is continuous-time, the communications between every two different nodes are discrete-time, i.e., they are active only at some discrete time instants. Moreover, the communication intervals between every two communication instants can be uncertain and variable. By choosing a piecewise Lyapunov-Krasovskii functional to govern the characteristics of the discrete communication instants and by utilizing a convex combination technique, a synchronization criterion is derived in terms of linear matrix inequalities with an upper bound for the communication intervals obtained. The results extend and improve upon earlier work. Simulation results show the effectiveness of the proposed communication scheme. Some relationships between the allowable upper bound of communication intervals and the coupling strength of the network are illustrated through simulations on a fully connected network, a star-like network, and a nearest neighbor network.

Adaptive pinning cluster synchronization of fractional-order complex dynamical networks

The problem about cluster synchronization of fractional-order CDNs is studied via a pinning adaptive approach in this paper. Based on the stability theory of fractional differential equations, some sufficient criteria for local and global cluster synchronization of fractional-order CDNs are derived. In this paper, the coupling configuration matrix can be asymmetric as well as reducible and the inner coupling matrix can also be asymmetric. Moreover, the number of pinning nodes in each cluster can be evaluated. Especially, when the coupling strength is large enough and the coupling configuration matrix is symmetric, cluster synchronization can be achieved via pinning a single node in each cluster. Finally, some typical examples are given to illustrate the correctness and effectiveness of our results, a surprising finding is that the synchronization performance will become better as the fractional order decreases in this simulation.

Impulsive Multisynchronization of Coupled Multistable Neural Networks With Time-Varying Delay

This paper studies the synchronization problem of coupled delayed multistable neural networks (NNs) with directed topology. To begin with, several sufficient conditions are developed in terms of algebraic inequalities such that every subnetwork has multiple locally exponentially stable periodic orbits or equilibrium points. Then two new concepts named dynamical multisynchronization (DMS) and static multisynchronization (SMS) are introduced to describe the two novel kinds of synchronization manifolds. Using the impulsive control strategy and the Razumikhin-type technique, some sufficient conditions for both the DMS and the SMS of the controlled coupled delayed multistable NNs with fixed and switching topologies are derived, respectively. Simulation examples are presented to illustrate the effectiveness of the proposed results.

Stability analysis of switched positive linear systems with stable and unstable subsystems

This paper addresses the stability problem of switched positive linear systems with stable and unstable subsystems. Based on a multiple linear copositive Lyapunov function, and by using the average dwell time approach, some sufficient stability criteria of global uniform exponential stability are established in both the continuous-time and the discrete-time cases, respectively. Finally, some numerical examples are given to show the effectiveness of the proposed results.

IMPULSIVE CONTROL FOR T–S FUZZY SYSTEM AND ITS APPLICATION TO CHAOTIC SYSTEMS

An impulsive T–S fuzzy model is presented in this paper. The stability of impulsive controlled T–S fuzzy system has been analyzed theoretically. The proposed impulsive control scheme seems to have a simple control structure and may need less control energy than the normal continuous ones for the stabilization of T–S fuzzy system. Some typical chaotic systems, such as Chuas circuit, Lorenz system and Chens chaotic system, are considered as illustrations to demonstrate the effectiveness of the proposed control scheme.

Adaptive pinning control for the projective synchronization of drive-response dynamical networks ☆

Abstract This paper studies the projective synchronization of a drive-response dynamical network of partially linear systems. The coupling-configuration matrix of the network is not necessarily symmetric. Two adaptive pinning control strategies are derived based on the Barbalat’s Lemma. In the first control strategy, the pinning control gain is adaptively updated to realize the projective synchronization. In the second control strategy, both the pinning control gain and the coupling strength between nodes are adaptively updated. Numerical simulation results show that the coupling strength needed in the second control strategy is smaller than that in the first control strategy to achieve the projective synchronization of the network.

Synchronisation of complex dynamical networks with additive stochastic time-varying delays

In this letter, a class of complex dynamical networks with additive stochastic time-varying delays is investigated. Two kinds of delays in complex dynamical networks are taken into consideration, one is called the nodes-induced delay in this paper, and the other is the network-induced delay. Both of the delays are assumed to obey different stochastic distributions. By utilising a novel Lyapunov–Krasovskii functional and stochastic analysis techniques, a sufficient criterion is obtained in the form of linear matrix inequalities to ensure the synchronisation of the complex dynamical networks. Finally, a numerical example is given to illustrate the feasibility and effectiveness of the proposed method.

Reaching cluster consensus in multi-agent systems

In this paper, the cluster consensus problem of linearly coupled multi-agent systems in directed networks is studied by constructing a Laplacian of a directed graph. Different from the former work in which the clusters are divided artificially, in this paper, the relationship between the number of the clusters and the Laplacian is revealed. It is obtained that the number of clusters equals to the multiplicity of the zero eigenvalue of the Laplacian. Based on the Algebraic Graph Theory, the Matrix Theory and the Modern Control Theory, a sufficient and necessary condition about the global stability of the cluster consensus in multi-agent system is derived. A numerical example is proposed to illustrate the effectiveness of the method.