Stability Analysis Of Linear Time-varying Delays Systems Under Asynchronous Switching

As an important hybrid dynamical system,switching system is widely used in electrical power system,traffic control and engineering control.With the rapid development of science and technology,scholars have studied switched systems in depth,and it has achieved fruitful results.However,in previous discussions on switching systems,the scholars assumed that the switching time of subsystems is the same as the switching time of controllers,but the system needs time to identify subsystems and select corresponding controllers in practice,which results in delays of the switching of controllers,so that the switching of subsystems does not match the switching of controllers at a certain period of time.In this paper,the asynchronous switching problem of linear systems is studied.The purpose of this paper is to study the asynchronous switching problem of linear systems.The main contents are as follows:In the first chapter,the related contents of hybrid dynamical systems,switching system and asynchronous switching are introduced briefly.At the same time,the importance of stability in switching system is analyzed.Some definitions related to the content of the paper are given.The main research contents of this paper are explained.Finally,the relevant numerical symbols are given.In the second chapter,a linear switched system with uncertain time-varying delays is discussed,the robust exponential stability of the system under asynchronous switching is also studied.By constructing a new Lyapunov function and matrix inequality,and with the average dwell time is used to constrain the system.Sufficient conditions for robust exponential stability of a given system under asynchronous switching are obtained,and on this basis,the controller gains for stabilizing the system are obtained.In the third chapter,sufficient conditions for robust stability of linear switched systems with input delays under asynchronous switching are discussed.A newcriterion for exponential stability of the closed-loop system is established by the average dwell time method,the double integral piecewise Lyapunov function and the multinomial lemma.The corresponding controller gains of the system are obtained by using the LMIs.