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Finite-time stability theorem of stochastic nonlinear systems. (English) Zbl 05850219
Summary: A new concept of finite-time stability, called stochastically finite-time attractiveness, is defined for a class of stochastic nonlinear systems described by the ItĂ´ differential equation. The settling time function is a stochastic variable and its expectation is finite. A theorem and a corollary are given to verify the finite-time attractiveness of stochastic systems based on Lyapunov functions. Two simulation examples are provided to illustrate the applications of the theorem and the corollary established in this paper.

MSC:
93E15Stochastic stability
93D05Lyapunov and other classical stabilities of control systems
93C10Nonlinear control systems
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References:
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