Criteria for practical stability in the \(p\)th mean of nonlinear stochastic systems.

*(English)*Zbl 0755.93080Summary: 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:

93E15 | Stochastic stability in control theory |

93C10 | Nonlinear systems in control theory |

93E03 | Stochastic systems in control theory (general) |

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\textit{Z. Feng} et al., Appl. Math. Comput. 49, No. 2--3, 251--260 (1992; Zbl 0755.93080)

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