Delay-dependent Stability for Vector Nonlinear Stochastic Systems with Multiple Delays

Global asymptotic stability conditions for vector nonlinear stochastic systems with multiple state delays are obtained based on the convergence theorem for semimartingale inequalities, without assuming the Lipschitz conditions for nonlinear drift functions. Obtaining the delay-dependent stability conditions for nonlinear stochastic time-delay systems leads to a significant advantage in the nonlinear control theory and practice, since it enables one to address the stabilization problems for nonlinear systems, influenced by stochastic disturbances, whose dynamics is subject to multiple time delays in nonlinear functions, which make the LMI technique inapplicable. The LyapunovKrasovskii 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.