Finite Time Control Of Discrete Time Stochastic Systems

In recent years,the finite time control problem has been a research hotspot in the field of control.The main research focuses on the finite time stability analysis and robust controller design of the system.The point of finite time control is to improve the transient performance of the system.On the other hand,due to the development of computer technology,discrete-time system has also attracted the interest of scholars,including optimal control,robustness,deadbeat control,sampling control and so on.In this paper,the finite time control problem of discrete-time stochastic system is studied as follows:(1)The stability and stabilization of discrete-time stochastic systems in finite time domain are studied.The state feedback controller,the static output feedback controller and the dynamic output feedback controller are designed respectively to make the closed-loop system stable in the finite time domain.Finally,a numerical example is given to illustrate the feasibility of the design method.(2)The problem of the finite-time annular domain stability and stabilization of discrete-time stochastic systems with disturbance is studied.A definition of finite-time annular domain stability for discrete-time stochastic systems has been given.And the state feedback controller and observer-based controller have been designed.(3)The problem of the stochastic finite-time control for discrete-time stochastic Markov jump systems is studied.The sufficient conditions for the stability of discrete-time stochastic systems are proposed,such that the discrete-time stochastic system is finite-time annular domain stable.And we will prove the existence conditions of state feedback controller and observer-based controller.Finally,a simple example is given to illustrate the feasibility of the method.(4)The finite-time H? control problem for discrete-time stochastic Markov jump systems is investigated.Firstly,the definition of finite time H? control is given,and the sufficient conditions for the existence of finite time state feedback controller and output feedback H? controllers are obtained by using matrix transformation technology,which ensure that the system not only satisfies the boundedness of finite time,but also satisfies the H? performance index.