## 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

### Keywords:

stochastic differential system; asymptotic stability
Full Text:

### References:

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