Control Of The Stability For Stochastic Systems

Stochastic systems have been studied for several decades. Stochastic stability as a basic requirement for system to be operated normally, has attracted people's interest widely and acquired a lot of important conclusions recently. But the ordinary study for the stability is concentrating on the asymptotic mean squire stable, which studies the characters of the infinite time interval of the system. However, in practice, people are sometimes concerning with the characters of a finite time interval for the system. In this sense, it's reasonable to study a system whose state, given some initial conditions, remains within prescribed bounds in fixed time interval, this is the so-called finite-time stable problem.Using the method of linear matrix inequality, the paper studies the finite-time stabilizable for the continuous-time stochastic systems, then it studies the finite-time stochastically robust stabilizable via state feedback and the finite-time stochastically stabilizable via output feedback for the discrete-time stochastic systems.Firstly, we study the finite-time stabilizable for a kind of continuous-time stochastic systems, and provide the sufficient conditions for the systems to be finite-time stochastically stabilizable via static and dynamic output feedback respectively. These conditions are eventually reduced to the feasibility problems of linear matrix inequalities.Secondly, we study the finite-time control for the discrete-time stochastic systems. We provide the sufficient conditions for the system to be finite-time stochastically robustly stabilizable via state feedback, which can be applied to problems with both non-zero initial conditions and unknown exogenous disturbances; Then we give the sufficient conditions for the system to be stochastically stabilizable via static and dynamic output feedback respectively, and the conditions are transformed to the problems of the existence of the solution to the linear matrix inequalities. At last, some examples are given to illustrate the importance of our results.