Variable structure control of stochastic systems (Q1319502)

Variable structure control (VSC) using sliding modes has been studied for many years, and its robustness properties with respect to unknown parameters and deterministic disturbances are well-known. The present paper extends VSC theory to discrete-time stochastic systems, assuming an additive Gaussian noise with mean zero. First, systems with complete state information are considered. Conditions are derived under which the trajectory is driven to and held in a given band with a prescribed probability using VSC. Then, for systems with incomplete state information, an algorithm of Kalman filter type for state estimation is proposed, and the asymptotic properties of the over-all VSC systems are discussed. Various simulation results portray the effectiveness of the proposed method.