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Zbl 1229.93159
Abedi, Fakhreddin; Abu Hassan, Malik; Md Arifin, Norihan
Lyapunov function for nonuniform in time global asymptotic stability in probability with application to feedback stabilization. (English)
[J] Acta Appl. Math. 116, No. 1, 107-117 (2011). ISSN 0167-8019; ISSN 1572-9036/e

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.
[Constantin Vârsan (Bucureşti)]

MSC 2000:: *93E15 Stochastic stability
60H10 Stochastic ordinary differential equations
93C10 Nonlinear control systems
93D05 Lyapunov and other classical stabilities of control systems
93D15 Stabilization of systems by feedback
93D21 Adaptive and robust stabilization

Keywords: stochastic differential system; asymptotic stability

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