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

93E15Stochastic stability
60H10Stochastic ordinary differential equations
93C10Nonlinear control systems
93D05Lyapunov and other classical stabilities of control systems
93D15Stabilization of systems by feedback
93D21Adaptive or robust stabilization
Full Text: DOI
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