Stability Analysis Of Fractional-order Impulsive And Switched System

In this paper,we study the stability of fractional-order system from three parts.In first part,the asymptotic stability and finite-time stability of fractional-order nonlinear system are studied.The second part studies the asymptotic stability of fractional-order switched system with stable subsystems and the asymptotic stability and finite-time stability of fractional-order switched system with unstable subsystems.The third part studies the asymptotic stability and finite-time stability of fractional-order impulsive and switched system.In the first part,this paper studies the asymptotic stability of fractional-order system with nonlinear perturbation and nonlinear system with the controls.By using the Gronwall integral inequality,theorem is given to verify finite-time stability of a class of nonlinear system.In the second part in this paper,the equivalent integral equation of fractional-order switched system is investigated firstly.Asymptotic stability of fractional-order switched system is studied by using the method of multiple Lyapunov functions.By combining with the technique of dwell time and average dwell time,sufficient conditions are given to verify the asymptotic stability of fractional-order switched system with stable subsystems and the asymptotic stability and finite-time stability of fractional-order switched system with unstable subsystems.Finally,numerical simulations of some examples are given to make switched system stable by switching law satisfying the conditions,and verify the correctness of theorems.In the third part,by using the method of multiple Lyapunov functions,combining the definitions of dwell time and average dwell time,the asymptotic stability of fractional-order impulsive and switched system with stable subsystems is studied,finite-time stability of fractional-order impulsive and switched system with unstable subsystems are obtained.Finally,the impulsive and switched system is asymptotically stable and finite-time stable by switching law satisfying the conditions in numerical simulations of some examples,the correctness of the theorem is verified.