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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.

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
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