Abstract
In this study, we investigate the stochastic finite-time stability theory and finite-time stabilization of stochastic time-varying nonlinear systems with Markovian switching in the sense of weak solutions. First, we present the stochastic finite-time stability theory under the framework of weak solutions: the existence of weak solutions and stochastic finite-time stability theorems for stochastic time-varying nonlinear systems with Markovian switching. Second, for a class of high-order stochastic nonlinear systems with Markovian switching, a finite-time stabilization controller is constructively designed, and the trivial weak solution of a closed-loop system is proven to be globally finite-time stable in probability. The effectiveness of the proposed finite-time control method is illustrated by a numerical example.
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This work was supported by National Natural Science Foundation of China (Grant Nos. 61673284, 61807017).
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Zhao, GH., Liu, SJ. Finite-time stabilization of nonlocal Lipschitzian stochastic time-varying nonlinear systems with Markovian switching. Sci. China Inf. Sci. 65, 212204 (2022). https://doi.org/10.1007/s11432-021-3458-9
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DOI: https://doi.org/10.1007/s11432-021-3458-9