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Criteria for practical stability in the \(p\)th mean of nonlinear stochastic systems. (English) Zbl 0755.93080
Summary: A new concept, practical stability, in the \(p\)th mean, is proposed for nonlinear stochastic systems. By using the Lyapunov-like functions and the basic comparison principle for stochastic systems, criteria are established for various types of practical stability in the \(p\)th mean of nonlinear stochastic systems. These criteria make it possible to determine the practical stability in the \(p\)th mean of the nonlinear stochastic systems by testing the practical stability of the corresponding auxiliary deterministic systems.

93E15 Stochastic stability in control theory
93C10 Nonlinear systems in control theory
93E03 Stochastic systems in control theory (general)
Full Text: DOI
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