Finite-Time Stabilization of Stochastic High-Order Nonlinear Systems

This paper considers the problem of global finite-time stabilization in probability for stochastic high-order nonlinear systems in which the power order is greater than or equal to one and the drift and diffusion terms satisfy weaker growth conditions. Based on stochastic Lyapunov theorem on finite-time stability, via the combined adding one power integrator and sign function method, constructing a C2 Lyapunov function and verifying the existence and uniqueness of solution, a continuous state feedback controller is designed to guarantee the closed-loop system globally finite-time stable in probability.