Finite-time Stabilization for a Class of Stochastic Nonlinear Systems with Markovian Switching

The finite-time stabilization for a class of stochastic nonlinear systems with Markovian switching and uncertain transition probabilities is studied in this paper. Different from existing results for stochastic systems with Markovian switching which are all about strong solutions, the results in this paper are about weak solutions. Firstly, we develop Lyapunov theorems for the existence of a global weak solution and finite-time stability in sense of weak solutions respectively for stochastic nonlinear systems with Markovian switching in this paper. Secondly, a common finite-time controller via state-feedback is constructively designed by the cifinnion coordinate transformation of all subsystems and the method of adding a power integrator for a class of stochastic nonlinear systems with Markovian switching and uncertain transition probabilities. It is shown that the closed loop system has a global weak solution and the zero solution is finite-time stable globally in probability by the developed finite time stability theorem. At last, a numerical example is provided to illustrate the effectiveness of the proposed design method.