NEW RESULTS ON ROBUST STATE BOUNDING ESTIMATION FOR DISCRETE TIME MARKOVIAN JUMB STOCHASTIC CONTROL SYSTEMS

Abstract

The paper deals with the robust state bounding estimation problem of stochastic control systems with discrete time Markovian jump. By using Lyapunov functional method and probability theory, we propose new sufficient conditions to guarantee robust state boundedness for the stochastic control systems. The conditions are derived in terms of linear matrix inequalities, which is simple and convenient for testing and application. Unfortunately, difficulties arise when one attempts to derive the sufficient conditions and to extract the controller parameters for these systems. In fact, we have to cope with stochastic process and disturbance. Indeed, the Lyapunov functional method is a powerful tool to stability analysis of differential systems. However, this method is not effectively applied for stochastic systems because we do not know how to construct suitable Lyapunov functions and use them in these systems. To overcome the difficulties, we first introduced basic concepts of probability theory. Next, a new sufficient conditions of robust state boundedness for unforced stochastic systems was established. Finally, the result was applied to design controllers to guarantee robust state boundedness for stochastic control systems.