Lyapunov function for nonuniform in time global asymptotic stability in probability with application to feedback stabilization. (English) Zbl 1229.93159

Abedi, Fakhreddin; Abu Hassan, Malik; Md Arifin, Norihan

Acta Appl. Math. 116, No. 1, 107-117 (2011).

The aim of this paper is to extend the well known Artstein-Sontag theorem to the concept of stochastic control Lyapunov function when nonuniform in time stochastic systems are considered. A stabilizer for a wider class of SDE is designed. The main tools used here are the stochastic Lyapunov theorem proved by Khasminsskii and La Salle’s invariance theorem.

Reviewer: Constantin Vârsan (Bucureşti)

MSC:

93E15	Stochastic stability in control theory
60H10	Stochastic ordinary differential equations (aspects of stochastic analysis)
93C10	Nonlinear systems in control theory
93D05	Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory
93D15	Stabilization of systems by feedback
93D21	Adaptive or robust stabilization

Keywords:

stochastic differential system; asymptotic stability

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