A new LMI observer-based controller design method for discrete-time LPV systems with uncertain parameters

This paper deals with observer-based controller design problem for discrete-time Linear Parameter Varying (LPV) systems with uncertain parameters. The proposed technique consists in designing an observer-based controller which stabilizes the LPV system, provided that the norm of the difference between the measured parameter and the real one does not exceed a tolerated maximum value. The particularity of the proposed design method, compared to some existing methods in the literature, is that it works on one systematic step, without any a priori choice of some observer-based controller parameters. The solution is formulated in terms of a single set of Linear Matrix Inequalities (LMIs). Besides, a relaxation of the proposed design with respect to the uncertainty is provided. The proposed approach is compared with other similar stabilization approaches, through two numerical examples.