Gain Scheduled Hâˆ‍ Control for Linear Parameter Varying Stochastic Systems

Abstract

In this paper, a gainscheduled controller design method is proposed for linear parameter varying (LPV) stochastic systems subject to Hâˆ‍ performance constraint. Applying the stochastic differential equation, the stochastic behaviors of system are described via multiplicative noise terms. Employing the gainscheduled design technique, the stabilization problem of LPV stochastic systems is discussed. Besides, the Hâˆ‍ attenuation performance is employed to constrain the effect of external disturbance. Based on the Lyapunov function and Itأ´'s formula, the sufficient conditions are derived to propose the stability criteria for LPV stochastic systems. The derived sufficient conditions are converted into linear matrix inequality (LMI) problems that can be solved by using convex optimization algorithm. Through solving these conditions, the gainscheduled controller can be obtained to guarantee asymptotical stability and Hâˆ‍ performance of LPV stochastic systems. Finally, numerical examples are provided to demonstrate the applications and effectiveness of the proposed controller design method.