Stability And Sychronization Control For Switched Complex Networks

The main features of complex networks are that nodes are used to represent different individuals in real systems and edges to represent the mutual relations among individuals.Based on these features,complex networks can be applied to represent large-scaled systems in nature,human society,and engineering.In the face of various complex networks,some external and internal factors often lead to systems with "switch" phenomena,such as changes in the network environmen-t,damage to system components,sudden change in system control inputs,packet dropout,random failure and malicious attacks in the process of networked control,etc.From mathematical point of view,switched complex networks can describe com-plex networks with switched local dynamical behavior or switched network topology.This dissertation formulates various switched phenomena for complex networks by switched systems approaches,and establishes some corresponding switched com-plex networks,then studies stability and synchronous control problems for switched complex networks.In this dissertation,we focus on switch phenomena in local dynamics,network topology and control data,and use Lyapunov stability theory,time-delayed system approach,switched system method,graph theory and linear matrix inequality technique,etc.The detailed results of this dissertation are as follows:(1)The stochastic stability for a class of discrete-time switched neural networks is analyzed,in which time-varying mixed delays and stochastic noise are considered.Specifically,the stability criterion for discrete-time neural networks with time-varying distributed delays is obtained on the basis of a Lyapunov functional with the triple summation term.Subsequently,in view of average dwell time approach and stochastic analysis,several sufficient conditions are obtained to ensure that the mean square stability problem for switched neural networks is solvable.Furthermore,the derived sufficient conditions reflect that the decay rate of the considered neural networks is relative to average dwell time,upper and lower bounds of delays and intensity of stochastic noise.(2)The synchronization problem for a class of directed switched complex net-works is inveatigated.The links among the nodes are perturbed by stochastic noises and the topology varies according to certain predetermined switching rules.The coupled networks under consideration are subjected to mixed delays compris-ing both discrete and distributed ones.A new estimate of the general algebraic connectivity is firstly given for the directed complex networks,based on which the exponential synchronization problem is analyzed by virtue of the average-dwell-time technique.Then,sufficient conditions are derived to guarantee the synchronization in mean square provided that the switching is slow on the average.Subsequently,the switched complex networks with link failures are investigated and it is shown that the synchronization can be achieved if the average link failure ratio does not exceed certain threshold.(3)We are concerned with the consensus for a class of nonlinear multi-agent systems with weak topology.The considered weak topology is assumed to be sequen-tially connected,and can be described to be some directed disconnected switched topologies with the aid of graph theory.Additionally,the combinational measure-ment approach is adopted to develop event-triggering strategy such that each agent updates control rule only at its own event-triggering instants.Firstly,by using the iterative method,we establish the recursive relationship of maximal distance sequence.Then,sufficient conditions of event-based bounded consensus can be obtained under the contractive condition of maximal distance sequence.Further-more,as an extension,we consider the case of jointly connected topology,and the corresponding consensus problem is also explored.(4)The state estimation problem is considered for a class of delayed complex networks with intermittent sampled-data.Due to some network factors,transmis-sion of sampled-data may fail through communication networks.Hence,intermit-tent transmission of sampled-data is considered in this chapter.Specifically,the error system is first transformed into time-varying delayed switched systems,in-cluding both stable and unstable subsystems.And then,to analyze the stability of the error system,a modified Halanay inequality is presented.In view of the modified Halanay inequality and switched systems method,sufficient conditions for globally exponential stability of the error system are established.Meanwhile,the upper bound of transmission failure rate is given,which is relative to sampling pe-riod and the upper bound of node delays.Furthermore,the desired estimator gain of each node is explicitly provided by solving a set of matrix inequalities.(5)The sampled-based consensus problem is investigated for a class of nonlinear multi-agent systems subjected to cyber-attacks.Due to network fluctuations and limited resources,deception attacks might destroy the sampled-data in systems.The purpose of this chapter is to design the sampled-based protocol such that the multi-agent systems under deception attacks can achieve mean square consensus.Firstly,the eigenvector of Laplacian matrix is utilized to construct a novel Lyapunov functional.Then,the decoupled criterion connected with eigenvalues of Laplacian matrix is obtained such that the addressed multi-agent systems achieve the mean square consensus.Furthermore,the solutions of a set of matrix inequalities represent the controller gain matrix.