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Zbl 0755.93080
Feng, Zhaoshu; Liu, Yongqing; Guo, Fengwei
Criteria for practical stability in the $p$th mean of nonlinear stochastic systems. (English)
[J] Appl. Math. Comput. 49, No.2-3, 251-260 (1992). ISSN 0096-3003

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.

MSC 2000:: *93E15 Stochastic stability
93C10 Nonlinear control systems
93E03 General theory of stochastic systems

Keywords: practical stability; nonlinear stochastic systems; Lyapunov-like functions

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