Stabilization of nonlinear stochastic discrete systems

Abstract : Our goal is to give a sufficient condition for feedback stabilization of nonlinear stochastic discrete systems. The stabilization problem of both continuous-time and discrete-time deterministic nonlinear control systems has attracted the interest of an increasing number of authors in the last decades and various techniques have been developed to design stabilizing feedback. As for stabilization of stochastic nonlinear control systems, only few results are available in the literature. Properties of the solution of the stochastic algebraic Riccati equation introduced by Wonham (1968) are used by Gao and Ahmed (1987) to deal with the stabilizability problem for a class of continuous-time stochastic nonlinear control systems. More recently, by using the Lyapunov functions method, a stochastic version of Artstein-Sontag's theorem is established in Chabour and Oumoun (1999), while a Jurdjevic-Quinn type theorem is stated in Bensoubaya et al. In this paper we give a sufficient condition for global stabilization of discrete-time stochastic systems. This condition is the discrete analogue of the Jurdjevic-Quinn type condition derived in Bensoubaya et al. for continuous-time stochastic control systems.