Stability Analysis Of Several Kinds Of Switched Systems

A switching system is usually composed of multiple differential equations or difference equations and a switching strategy to control the switching between them.The research on stability is also the most important part of the switching system,many properties of research are based on stability.In practical applications,there are often unstable subsystems in the switching system that interfere with the stability of the system,so considering the stability of the switching system with unstable subsystems has become a hot issue in this field.This article has completed the following content:(1)The switching control of linear systems has been studied,and many scholars have done related research on such problems.In recent years,some scholars are more concerned about whether the system can be stabilized by switching control when the system is unstable(that is,a state feedback controller cannot be found to keep the closed-loop system stable).Related research results often appear in core journals.We have also conducted in-depth research on this issue,and have obtained research results different from other scholars.The result is that for unstable systems,it is impossible to stabilize them by switching control.(2)The stability of switching system based on all subsystems unstable is studied.On the basis of studying the discrete Lyapunov functional method proposed by predecessors,a feasible method of discretization parameter dependent Lyapunov functional(DPDLFs)was proposed.An appropriate dwell time switching rule is designed,and the criterion for asymptotic stability of the system under this switching rule is given.Finally,a numerical example shows that the the conclusion is correct.(3)The stability of switched singular time-delay systems in which all subsystems are unstable is studied.First,we discuss the case where the delay term is constant and relax the assumption that the delay term of the system is less than the constant multiple linear term.By constructing the discretized Lyapunov-Krasovskii functional,combined with the dwell time frame.A sufficient condition for the asymptotic stability of switched singular time-delay systems is derived based on matrix inequalities.The above method is applied to a system with variable time delay to obtain sufficient conditions for the asymptotic stability of the system.(4)Finally,the unstable subsystem switching methods discussed in 2 and 3 are applied to consider the stability of switched nonlinear time-delay systems where all subsystems are unstable.Similarly,the two cases of constant delay and variable delay are analyzed separately,and the rationality of the switching rule design under the asymptotic stability of the system is obtained.Finally,a given two-dimensional numerical example illustrates the correctness of the method.