Stabilization of Stochastic Linear Systems via Path-dependent Feedback Control

Abstract

This paper aims to investigate the stabilization problem of stochastic linear system via path-dependent state-feedback control. For the given stochastic linear system, a novel feedback control is designed with the path-dependent information of the system states, and the control gains are determined by the stochastic algebraic Riccati equation. To prove that path-dependent control can drive the stochastic linear system to be exponentially stable, a novel Lyapunov function is proposed. Combined with the general theory on stability of stochastic system, it is shown that stochastic system will be stabilized in mean-square via path-dependent control.