Research On Finite-Time Stability Analysis And Control Of Impulsive Stochastic Systems

In recent years,many scholars paid more and more attention on the hybrid systems,because it can not only represents many complicated systems in the real world,but also has a significant value and engineering practice background in theoretical research.Impulsive stochastic system as an important hybrid system,which provides a lot of research topics in the field of system engineering and control.And it has attracted much attention of many scholars both here and abroad.In addition,the system such as communication network system,robot control system,missile system,which acting in a short time interval and quick response,the finite-time stability is more important than asymptotic stability.This paper mainly deals with finite-time stability and control design problems of impulsive stochastic systems,the details are as follows:1.The problems of finite-time stability and control for a class of linear impulsive stochastic delayed systems is considered.Firstly,based on the finite-time stability theory,using Lyapunov-Krasovskii functional and Lyapunov function method,combined with delayed differential inequality and related lemmas respectively,two sufficient conditions with average impulsive interval constraint are established for the mean square finite-time stability of the underlying systems.Then,the stability sufficient conditions of two methods has been analyzed and compared.And based on sufficient conditions for finite-time stability,the design of the stabilization controller via state feedback is given in the form of linear matrix inequalities(LMIs).Finally,a numerical examples and image simulation is given to illustrate the effectiveness of our results.2.The finite-time stability and control problems for nonlinear impulsive stochastic systems with time-varying delays is further addressed.First of all,the sufficient conditions in the form of LMIs for the mean square finite-time stability are obtained by establishing the appropriate delay-dependent Lyapunov-Krasovskii functional method and appropriate inequality technique.Then,based on the proposed condition,state feedback controller is designed to ensure that the corresponding closed-loop system is mean sequare finite-time stable.Finally,the feasibility of the conclusion are verified by a numerical examples and image simulation.3.Considering that H?control theory as an important role in disturbance attenuation,the finite-time H?control problem for a class of impulsive stochastic systems is investigated.First of all,based on the H?theory control and Lyapunov function method,combined with the related lemmas,matrix analysis and average impulsive interval technique,sufficient conditions for mean square finite-time stability and mean square finite-time boundedness is proposed in terms of LMIs.Thenthe finite-time H?performance of the system is analyzed.Futhermore,the finite-time H?state feedback controller is designed,which can guarantee that the closed-loop system is mean square finite-time boundedness with a H?prescribed performance index.Finally,a numerical examples and image simulation is given to verify the effectiveness of the proposed controller.