Stability Analysis For Complex Networks And Switched System On Time Scales

Recently,complex networks and switched systems have attracted many researchers from physics,biology,economics and so on.The stability of complex networks and switched systems has been one of the heat issues in complexity science.However,in practice,we often encounter the phenomenon that the system undergoes continuous,discontinuous or intermittent dynamical evolutions,the theory of calculus on time scales can reveal the dynamic properties of the systems on hybrid time domains.Therefore,there exist important academic merits and extensive application basis to study the stability of complex networks and switched systems on time scales.This thesis principally analyzes the stability of complex networks and switched system on time scales.The main contents and research outputs of this thesis are threefold.(1)The stability for discrete complex networks with switching and delayed coupling is discussed.Based on Lyapunov stability theory,the sufficient conditions are derived by using LMI method for the asymptotic stability.Moreover,we establish the conve combination conditions for asymptotic stability of the networks and give the way to choose switching strategy.(2)A unified consensus problem for multi-agent networks by sampleddata control with missing packets on time scales is studied.By the theory of calculus on time scales,Lyapunov functional method and inequality technique,we obtain scale-type consensus for multi-agent networks which provides a unified frame for multi-agent networks on continuous,discrete and hybrid time domains.(3)The problem of stabilization for switched delay systems under asynchronous switching on time scales is studied.By constructing a piecewise Lyapunov-Krasovskii functional,sufficient conditions for scaletype stability are developed for a class of switching signals based on the average dwell time method.Finally,numerical simulations are given to illustrate the effectiveness of our new results.