Lyapunov stability and practical stability of nonlinear delay stochastic systems: a unified approach

In this paper, both Lyapunov stability in the pth mean and practical stability in the pth mean are defined for the delay stochastic systems. By applying the Lyapunov-like functions and the theory of differential inequalities, comparison principles are set up for the nonlinear delay stochastic systems. Based on these comparison principles, a unified approach is developed to deal with both the Lyapunov stability and the practical stability. Criteria are established for various types of Lyapunov stability and practical stability of the delay stochastic systems. By these criteria, the stability properties (Lyapunov and practical) of the delay stochastic systems can be obtained by testing the corresponding stability properties of the auxiliary delay deterministic systems.<
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