Abstract
ABSTRACT This article studies the finite time stability (FNTS) of time-varying nonlinear stochastic systems with random impulses. We provide sufficient conditions for the FNTS or even fixed time stability (FXTS) for time-varying stochastic systems under two cases: (1) The impulse time is deterministic; (2) The impulse time is random. For case (1), we use the reverse average dwell time to investigate FNTS, but for case (2), we employ the Poisson process theory to solve the stability problem. In addition, the stability criteria capture the stabilising effect of stochastic noise in the FNTS problem. Finally, the correctness of the theoretical results is verified with two numerical examples. As far as the author knows, no one has studied the FNTS of time-varying stochastic systems with random impulses.
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