Stability Analysis Of Fractional Order Switched Systems

Fractional order calculus is the generalization of integer order calculus,and t he former is more available than the latter for the behavior of systems.Stability is an important performance of the system,but.asymptotic stability and exponential stability reflect the behavior of the system in an infinite-time interval.In practice,sometimes we just need transient performance of system in finite-time interval.On the one hand,a system is stable,but its transient performance may not be stable.On the other hand,most of the system happen in finito-time interval.Therefore,it is necessary to study finite-time stability.However,finite-time stability requires the state does not,exceed a certain threshold over a appointed time interval.It should be put forward that sometimes only the output,not the state,needs to be restrained within a bound.Thus,the concept of input-output finite-time stability is put forward.Finite-time stability and input-output finite-time stability are used to reflect transient performance in finite-time interval.In normal systems,the average dwell time and Lyapunov function are often used to solve the control problem of switched systems.So far,this method is rarely used to fractional order switched systems.Therefore,this paper uses the average dwell time and Lyapunov function to solve the control problem of fractional order switched systems.The main work of this paper is summarized as follows:Chapter 2 studies finite-time stability and finite-time boundedness of fractional order switched systems.By employing average dwell time technique and Lyapunov function method,some sufficient conditions for finite-time stability and finite-time boundedness of FOSS are proposed.The state feedback controllers are constructed,and sufficient conditions are given to ensure that the corresponding closed-loop sys-tems are finite-time stable and finite-time bounded.These conditions can be easily obtained in terms of linear matrix inequalities.Finally,two numerical examples are given to show the effectiveness of the results.Chapter 3 studies input-output finite-time stability of fractional order switched systems.by using Lyapunov function method together with average dwell time ap-proach,some sufficient conditions of input-output finite-time stability for the consid-ered system and the corresponding closed-loop system are derived.These conditions can be easily obtained by linear matrix inequalities.Finally,two numerical examples are given to show the effectiveness of the theoretical results.Chapter 4 studies input-output finite-time stability of fractional order positive switched systems.by using co-positive Lyapunov function method together with average dwell time approach,some sufficient conditions of input-output finite-time stability for the considered system are derived.Furthermore,the state feedback controller and the static output feedback controller are designed,and sufficient con-ditions are presented to ensure that the corresponding closed-loop system is input-output finite-time stable.Finally,three numerical examples are given to show the effectiveness of the theoretical results.