New observer-based controller design for LPV stochastic systems with multiplicative noise

This paper addresses an observer-based control problem of Linear Parameter Varying (LPV) stochastic systems. Based on the modeling approaches, the LPV stochastic systems can be represented by a set of linear systems with multiplicative noise term. To solve the observer-based control problem, a less conservative stability criterion is developed via the chosen Parameter-Dependent Lyapunov Function (PDLF). In the PDLF, none element in the positive definite matrix is required as zero. Besides, an Extended Projection Lemma is proposed to convert the derived sufficient conditions into Linear Matrix Inequality (LMI) form. According to the derived LMI conditions, all feasible solutions can be found by convex optimization algorithm at a single step. Based on those feasible solutions, an observer-based Gain-Scheduled (GS) controller can be established to guarantee the asymptotical stability of the closed-loop system in the sense of mean square. Finally, two numerical examples are provided to demonstrate the effectiveness and applicability of the proposed method.