Stability Analysis Of A Class Of Interval Time-delay Switched Systems

Switched systems are a typical class of hybrid systems.Since it was proposed,it has been a research hot spot and has been widely used in the control field.Time delay and uncertainty are two important factors affecting the stability and performance of switched systems.The time delay of many practical systems is not only discrete but distributed or mixed,and only considering the switched system with discrete time delay is not enough to effectively describe and control the system.Therefore,it is of great theoretical significance to study the switched system with interval time delay（discrete time delay and distributed time delay）.In recent years,some scholars have studied the stability and control problems of interval time-delay switched systems through common or single Lyapunov function method,which is conservative.In this paper,the stability and feedback control of a class of interval time-delay switched systems are discussed by the average dwell time method.The contents are as follows:In the first chapter,the background and significance of switched systems,the background and current situation of interval time-delay switched systems,H_∞control theory,guaranteed cost control theory and average dwell time principle are introducedThe second chapter gives the definitions of exponential stability,guaranteed cost control and H_∞control,and the lemmas needed for proof.In the third chapter,the exponential stability of a class of switched systems with interval delay and uncertain interval delay is considered.By using the average dwell time method,and the inverse convex combination technique is introduced to deal with the linear matrix inequality.The exponential stability condition of the system is given,and the lower conservative upper bound of time delay is obtained by simulation.In the fourth chapter,the problem of guaranteed cost control for a kind of uncertain interval time-delay switched systems is considered.The guaranteed cost control law is designed.By using the average dwell time method and multi-Lyapunov functions,the system is exponentially stable and satisfies the upper bound J^（9）of guaranteed cost control.On this basis,the problem of guaranteed cost control for interval time-delay switched systems with multiple delays is considered.In the fifth chapter,the H_∞control problem of a class of switched systems with interval time delay is considered.The state feedback control law is designed,and the exponential stability condition and H_∞performanceγof the system are obtained by using the average dwell time method.Finally,summarize the work of this article and look forward to the future research direction.