Controller synthesis of linear parameter-varying stochastic systems based on gain-scheduled technique

摘要

This study discusses the controller synthesis of linear parameter varying (LPV) stochastic systems. In the description of this study, the multiplicative noise term is employed to represent stochastic behaviors of the system. For the issue of this study, two cases of Lyapunov function are employed. Through the Lyapunov functions and Ito's formula, the corresponding sufficient conditions are derived to discuss the stability and stabilization problems. Besides, the stabilization problem is dealt with by means of a gain-scheduled design technique to guarantee the stability of the system. For applying a convex optimization algorithm, the derived sufficient conditions are converted into linear matrix inequality form. With the proposed design methods, the LPV stochastic system driven by the designed controller is asymptotically stable in the mean square. Finally, numerical examples are provided to demonstrate the applicability and effectiveness of the proposed controller design methods.