Finite-time stabilization of nonlocal Lipschitzian stochastic time-varying nonlinear systems with Markovian switching

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.