Robust Control Of Stochastic Systems

Stochastic control, especially for the systems governed by Ito-type stochastic differential equations, has become a popular research field of modern control theory due to its great many applications in signal processing, mathematical finance and population modeling .First, this paper has clarified the relation among stochastic detectability, exact detectability and complete detectability via some examples. It is shown that stochastic detectability implies both exact detectability and complete detectability, but the converse is not true. Applying exact detectability to the study of stochastic LQ optimal control, the previous results are improved.Second, this paper is concerned with the H∞filtering design for discrete-time stochastic time-delay systems with state dependent noise. A sufficient condition for the existence of H∞filter design is presented via linear matrix inequalities.Finally, finite-time control problems for stochastic systems governed by Ito stochastic differential equations are considered. The main results provided are sufficient conditions for finite-time stochastic robust stabilization via state feedback. These conditions are eventually reduced to feasibility problems involving linear matrix inequalities (LMIs). One detailed example are presented to illustrate the validity of our developed theory.