Stability Analysis And Switching Stabilization Of Switched Systems

Stability is a key factor which can ensure normal running of practical systems.As a significant subject of control theory,stability analysis of(positive)switched systems has been widely concerned by experts and scholars in control field all over the world.However,most of the current results about stability of(positive)switched systems assume that all subsystems share a common equilibrium point.In fact,the influence of system itself or the external disturbance may lead to the phenomenon of multiple equilibrium points.Obviously,general(positive)switched systems with a common equilibrium point will be no longer suitable for describing the phenomenon,which motivates us to study the stability problem of(positive)switched systems with multiple equilibrium points.This paper investigates the stability problems of switched perturbation systems,positive switched systems with multiple equilibrium points and positive switched delay systems with a common equilibrium point.By using the method of Lyapunov function,the dwell time technique or by giving the solutions of considered systems,some sufficient conditions are presented for stability of(positive)switched systems with multiple equilibrium points.The main works are as follows:1.The regional stability problem of continuous-(discrete-)time switched per-turbation systems is studied.Each subsystem is assumed to have a unique equilib-rium point,and the system matrices of parts of subsystems are not Hurwitz(Schur)stable.Firstly,the solutions of considered systems under arbitrary switching signals are derived.Secondly,based on the Lyapunov function method and the dwell time technique,by restricting the size of ratio between the total dwell time of all unstable subsystems and the total dwell time of all stable subsystems,some sufficient con-ditions are presented for global asymptotic regional stability of considered systems.An effective method for estimation of stability region is also provided.2.The regional stability problem of continuous-(discrete-)time positive switched systems with multiple equilibrium points is studied.Each subsystem is assumed to have a unique and stable equilibrium point.Firstly,necessary and sufficient con-ditions are given for the positivity of considered systems under arbitrary nonneg-ative initial conditions and arbitrary switching signals.Secondly,by constructing appropriate copositive Lyapunov functions,some sufficient conditions are given for global asymptotic regional stability of considered systems under the predetermined convergence rate.For one and two dimensional systems,the corresponding accurate stability regions are proposed.3.The switching stabilization problem of continuous-(discrete-)time positive switched systems with multiple equilibrium points on finite time intervals is studied.Firstly,based on the definition of finite time stability about general positive switched systems,finite time stability of positive switched systems with multiple equilibrium points is given.Secondly,by constructing appropriate copositive Lyapunov func-tions,and restricting the size of ratio between the total dwell time of all unstable subsystems and that of all stable subsystems,some sufficient conditions are given for finite time stability of considered systems under constraint switching signals.4.The switching stabilization problem of continuous-(discrete-)time positive switched delay systems is studied.All subsystems are assumed to be unstable.By constructing multiple discretized copositive Lyapunov functions,and designing rea-sonable dwell time switching signals,some sufficient conditions are given for global asymptotic stability of considered systems under constraint switching signals.