Robust Control For Stochastic Interval Systems With Time-delay And Markovian Jumps

In the actual modeling process,except for the interference of random factors,there inevitably exist some estimates or observation errors,i.e.,parameter error.In order to describe the system accurately,we use interval to describe it,which we called stochastic interval systems.In recent years,the interval time-delay systems or stochastic interval systems with time-delay have attracted many studies.The stability of the system has always been an important subject of control theory,it includes Lyapunov stability,asymptotic stability,bounded input-bounded output(BIBO)stability,finite time stability and so on.In this paper,we consider a class of discrete time delay systems with Markovian jumps and a class of continuous time stochastic Markovian switched interval systems with time-delay,the robust stabilization and finite-time stochastic stabilization in Lyapunov sense are studied respectively.Then,the design method of the corresponding time-delay feedback controller is given,specifically include:(1)For a class of discrete-time stochastic interval systems with time-delay and Markovian jumping,the definition of(Q _i,S _i,R _i)-dissipative is given firstly.Through the equivalent transformation of the matrix,the interval matrix is transformed into an uncertain matrix.Then,by constructing Lyapunov-Krasovskii functional and Ito differential,obtained the sufficient conditions for the existence of robust controllers of stochastic interval system with time-delay,and the design method of the controller is given,which has memory function.(2)For a class of stochastic interval systems with time-delay and Markovian switching,the definition of the finite-time stochastic optimization performance index is given firstly,which includes finite-time stochastic dissipation,finite-time stochastic passive and finite-time stochastic robust H_?.Some sufficient conditions of finite-time stochastic dissipation are given,and gives the design method of finite-time stochastic dissipative controller with memory function.The effectiveness of the method is illustrated by numerical simulation.The research of this paper not only enriches the robust control theory of stochastic system,but also extends the approach for robust control of stochastic systems.It can be said that the model of this study is diverse and comprehensive.The numerical examples with simulations illustrate the validity of the results and the effectiveness of the proposed methods.