Finite-time stability and stabilization of stochastic nonlinear systems with Markovian switching

In this paper, we will investigate the finite-time stability and finite-time stabilization of stochastic nonlinear (SNL) systems with Markovian switching. Firstly, some proper criteria on finite-time globally asymptotically stable in probability (FGSP) are provided. Then, by adding a power integrator technique, a state-feedback finite-time controller is explicitly constructed. It is proven that, the equilibrium at the origin of the closed-loop systems is FGSP.