Exponential Stability Of A Class Of Switched Integral Systems With Delay

Switching system is an important hybrid system,which is widely used in mechanical system,network engineering system,aircraft system and so on.The integral system is an important branch of many engineering systems,which often exists in the additional dynamical system,the finite spectrum assignment controller and the difference operator of the neutral functional differential equation.With the progress of society and the rapid development of science and technology,the research on switched system and integral system has achieved fruitful results.In many engineering fields in real life,time delay is one of the main factors that affect the stability performance of the system.The coupling of switching and delay will lead to more complex dynamic behavior,so it is necessary to study the switched integral systems with delay.In this paper,the stability of a class of switched integral systems with delay is discussed.The specific arrangement is as follows:In the first chapter,we briefly introduce the related contents and research status of the hybrid dynamic system,the switched system and its stability problems,the integral delay system,analyze the necessity of the research on the stability of switched integral systems with delay.The related definitions used in this paper are also given in the first chapter.At the same time,several research methods are explained,which are single Lyapunov method,multiple Lyapunov method and average dwell time method.In the second chapter,the problem of exponential stability for a class of switched integral systems with delay is discussed.Firstly,the concept of switching is added to the integral delay system.By constructing a special kind of L-K functional which limits the upper and lower bounds of the delay,the problem of exponential stability of the switched integral systems with delay is solved.By effectively reducing the integral term,the system can get smaller conservative results,and then the exponential stability conditions of the switched integral systems with delay are obtained.At the same time,in order to ensure the exponential stability of the system under any switching,the design scheme of the switching law is given.At the end ofthis chapter,the corresponding example is given.Based on the second chapter,the third chapter discusses the problem of robust exponential stability for a class of uncertain switched integral systems with delay.In the operation of practical engineering,many uncertain factors will inevitably appear in the system,which will inevitably have an important impact on the analysis and control of the system.Therefore,the research on the robust stability of uncertain switched integral systems with delay has important theoretical value and practical significance.While constructing the L-K functional,we use the single Lyapunov method,the multiple Lyapunov method and the average dwell time method to construct the appropriate switching scheme,and finally obtain the sufficient conditions for the exponential stability of the system.