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On delay-dependent stability for a class of nonlinear stochastic delay-differential equations. (English) Zbl 1103.93043
Summary: Global asymptotic stability conditions for nonlinear stochastic systems with state delay are obtained based on the convergence theorem for semimartingale inequalities, without assuming the Lipschitz conditions for nonlinear drift functions. The Lyapunov-Krasovskii and degenerate functionals techniques are used. The derived stability conditions are directly expressed in terms of the system coefficients. Nontrivial examples of nonlinear systems satisfying the obtained stability conditions are given.

##### MSC:
 93E03 Stochastic systems in control theory (general) 93D20 Asymptotic stability in control theory 93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, $$L^p, l^p$$, etc.) in control theory
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