Mean Square Stabilizability of a Class of Nonlinear Stochastic Systems

In this work, we consider a class of discrete-time nonlinear stochastic control systems. By the use of proper mean square stabilizability and observability conditions, we are able to show the stabilizing property of both moving and infinite horizon quadratic optimal controllers. It is demonstrated that the m.s. stabilizability properties of these different types of controllers are equivalent and, therefore, the existence of the m.s. stabilizing controller of one type implies the existence of the other type with the same stability property. These results will allow the use of finite-stage solutions of a Riccati-like matrix equation in a stabilizing control design which may drastically reduce the computation time.