Stability Analysis For Cascade Switched Systems With Mixed Delays

Under some conditions many nonlinear systems can be converted to nonlinear cascade systems.Therefore,the control problem of nonlinear switched systems is an important topic in the control field.In the past 20 years,as an important switched system,the nonlinear switched systems have attracted agreat attention by many scholars,and many research results have been gotten.But in comparison,the research findings about cascade nonlinear switched systems with time delay under asynchrono-us switching is extremely limited.This paper studies exponential stability and finite-time bounded and finite-timeH_∞control problem for a class of cascade switched systems with mixed delays.The main contents are as follows:Firstly,we study the exponential stability problem of the cascade nonlinear switch-ed systems.By means of integral transformation,the average dwell time method and the Lyapunov function method,the sufficient conditions which guarantee the expone-ntial stability of such systems are achieved.Secondly,finite time bounded problem for discrete cascade switched systems is studied.The system contains mixed delay and control input.By means of Lyapunov-Krasovskii function and model-dependent average dwell time method,the sufficient conditions which guarantee the finite-time boundedness for this class of cascade systems are obtained under asynchronous switching.Finally,the finite time control problem for cascade discrete switched systems is studied.By using of the method of the model-dependent average dwell time method,the finite time control for such system is achieved under asynchronous switching.