Finite-time Ring Domain Stability Study Of Pulse Switching Systems

Impulsive switched system is a kind of important hybrid system.In recent years,it has caused people's concern due to its widely used in the field of automation control,process control,computer control and so on.So far,there has been a lot of relevant research conclusion about finite-time stability of the impulsive system and switched system.But the results about finite-time stability on impulsive and switched system are very little,and mainly concentrate in recent years.Research on the finite-time annular domain stability(FTADS)for the system is very few.Therefore,it has much important value for the research on the stability of the finite-time annular domain of impulsive and switched system.Based on the above discussion,we mainly study the following two different types of finite-time annular domain stability of the impulsive and switched system in this paper.The specific contents and research results are as follows:The first part we consider the FTADS of impulsive switched systems by using average impulsive switched interval and mode-dependent parameter approach(MDPA).The contributions of this article lie in the following aspects: First of all,we extend the concept of finite-time annular domain stable to impulsive switched system.Then the average impulsive interval is defined and sufficient conditions of finite-time annular domain stability for impulsive and switched system is given.At the same time,the effect of different impulsive intensity on the the system is analyzed.The effects of various impulsive strengths of the system differ.Even so,we still do not require the upper and lower bounds of the impulsive switched interval,and we can still confirm that the system exhibits FTADS.The second part we consider the FTADS of random impulsive asynchronous Markovian switched systems by using average impulsive switched interval and mode-dependent parameter approach.First of all,the conditions of the FTADS are given by a theorem under the condition that asynchronous segment and synchronous segment of nonlinear random Markovian asynchronous impulsive switched system are unstable and stable.And this result is extended to linear random Markovian asynchronous impulsive switched system.Further,we study the problem of FTADS under the condition that synchronous segment and asynchronous of nonlinear system segment are all unstable.This kind of circumstance is more complicated,so the conditions needed are much more strict.But it is still achievable.At the same time,we will also extend the result to linear random Markovian asynchronous impulsive switched system.