LMI-based discrete LPV controller design for systems with inherent couplings in the scheduling vector: Improved robustness and performance

Abstract

This work presents the design of controllers for discrete-time linear parameter-varying systems, particularly in scenarios where uncontrollable regions emerge within the polytope obtained by convex rewriting of a certain bounded region. Two fundamental aspects are addressed: the stability of the system and the enhancement of the controller performance and robustness. The most significant results include the proposal of a strategy to isolate the regions that are not reached by the trajectories of the system due to inherent couplings in the scheduling vector. The resulting control law ensures asymptotic stability under specific conditions, along with improved performance and robustness against perturbations through the use of $H_{\infty }$ and linear matrix inequalities regions. Two numerical examples illustrate the applicability and performance of the proposal.