On Stochastic Finite-Time Stabilization with Continuous State-Feedback Controllers

Abstract

This paper investigates finite-time stabilization of stochastic systems with homogeneous feedback controllers. In the finite-time stabilization problems, chattering-like behavior usually appears in the input signals due to stochastic noises when homogeneous feedback controllers are designed by backstepping-like methods. This study investigates the causes of the chattering-like behavior that appears in the homogeneous feedback controllers. Moreover, we present design approaches of controllers for the finite-time stabilization of stochastic systems based on homogeneity, with the objective of reducing the chattering-like behavior. Finally, the validity of the proposed controllers is investigated based on numerical experiments.