A Jurdjevic-Quinn-type theorem for stochastic nonlinear control systems

Abstract

We consider stochastic nonaffine nonlinear control systems = + ( ) + ( ) (written in the sense of Itô), being a standard Wiener process, for which we give a sufficient condition for global stabilization by a bounded smooth state feedback that is explicitly given. This condition generalizes the well-known Jurdjevic-Quinn result for deterministic affine control systems.Index Terms-Lyapunov functions, state feedback law, stochastic nonlinear control systems, stochastic stability. Publisher Item Identifier S 0018-9286(00)00814-X.

Feedback control optimization of nonlinear systems under random excitations

“…Florchinger [1] and Bensoubaya et al [2] studied the stability of the feedback control systems with the Lyapunov approach. Boulanger [3] studied the asymptotic stability of the feedback control of an Itô equation in probability.…”

Stabilization of nonlinear stochastic discrete systems

“…More recently, by using the Lyapunov functions method, a stochastic version of Artstein-Sontag's theorem is established in [2], while a Jurdjevic-Quinn type theorem is stated in [1]. In this paper we give a sufficient condition for global stabilization of discrete-time stochastic systems of the form (1). This condition is the discrete analogous of the Jurdjevic-Quinn type condition derived in [1] for continuous-time stochastic control systems.…”

“…In this paper we give a sufficient condition for global stabilization of discrete-time stochastic systems of the form (1). This condition is the discrete analogous of the Jurdjevic-Quinn type condition derived in [1] for continuous-time stochastic control systems.…”

“…Our goal is to give a sufficient condition for feedback stabilization of system (1). 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.…”

“…Properties of the solution of the stochastic algebraic Riccati equation intoduced by Wonham ([6]) are used by Gao and Ahmed ([3]) 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 [2], while a Jurdjevic-Quinn type theorem is stated in [1]. In this paper we give a sufficient condition for global stabilization of discrete-time stochastic systems of the form (1).…”