Finite-time Stability And Boundedness Of Continuous-time Switched Systems And Application

Switching systems is an important class of hybrid system.It consists of a family of subsystems and a switching law that orchestrates switching between these subsystems.In practice,it has a wide application background,and more and more control system are improve the control performance by adjust switching strategies.Therefore,more and more research results are emerging on the problem of switched systems control.So far,the results focus on Lyapunov asymptotical stability.However,in practice application,we usually pay attention to the transient behavior of a system over a finite time interval,instead of the qualitative behavior of switched systems over an infinite time interval.As a result,the research of finite-time stability has been gradually enriched in recent years.In this paper,we summarizes the main researches in the field of switched systems and finite-time control systematically.Based on the existing research,we have con-sidered the finite-time stability and boundedness of continuous switched system with finite-time unstable subsystems and its application on DC-DC converter.The main results are as follows:Firstly,by using a class of mode-dependent average dwell time method and multi-Lyapunov functions approach,the finite-time stability problem of nonlinear and linear continuous switched systems are studied in this paper,and the sufficient conditions are given to make the switched systems finite-time stability.For linear switched system,we got the LMI conditions to make systems finite-time stability.Secondly,considered the external disturbance,the finite-time boundedness prob-lem of unlinear and linear continuous switched systems axe studied.the sufficient con-ditions are given to make switched systems show finite-time boundedness performance.For linear switched system,we also got the sufficient conditions as LMIs.Furthermore,a state feedback controller were designed for the switched linear systems with external disturbance to make the system finite-time boundedness.In the rest of paper,the finite-time stability problem of switched affine system is studied,and the simulation of the switched affine system model of DC-DC converter is carried out.Based on the error switching affine systems,we designed switching laws by MDADT method making Buck converter system finite-time stability.Simulation examples are presented to show the effectiveness of theorems we given.