Lyapunov-like techniques for stochastic stability

Abstract

The purpose of this paper is to give a survey of the results proved in Florchinger (1993) concerning the stabilizability problem for control stochastic nonlinear systems driven by a Wiener process. Sufficient conditions for the existence of stabilizing feedback laws which are smooth, except possibly at the equilibrium point of the system, are provided by means of stochastic Lyapunov-like techniques. The notion of dynamic asymptotic stability in probability of control stochastic differential systems is introduced, and the stabilization by means of dynamic controllers is studied.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>