Feedback Stabilization of Stochastic Dynamical Systems Using Stochastic Dissipativity Theory

Abstract

In this paper, the feedback stabilization problem of nonlinear stochastic systems driven by Wiener processes is addressed. It is shown that the existence of a stochastic control Lyapunov function that guarantees the exponential mean square stabilization of the zero solution by linear static output feedback (SOF), under certain circumstances, is equivalent to the stochastic exponential dissipativity of the plant. Quadratic supply rates are proved to be general enough to establish this equivalence. Necessary and sufficient dissipativity-based conditions for stochastic asymptotic stabilization in probability via full state feedback are also given. In general, this work extends recently published results on dissipativity-based feedback stabilization of deterministic nonlinear systems to the problem of stochastic stability analysis and control of stochastic dissipative systems, a research topic within control theory that has been attracting growing interest. An illustrative example is offered as an application of the ideas presented in the article.