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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.

93E15Stochastic stability
93D05Lyapunov and other classical stabilities of control systems
93C10Nonlinear control systems
Full Text: DOI
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