LMI relaxations for robust gain‐scheduled control of uncertain linear parameter varying systems

Abstract

This study deals with the problem of robust gain-scheduled dynamic output feedback control for uncertain discrete-time linear parameter varying systems. The obtained controller guarantees an upper bound on the induced $l_2$l 2 -gain performance of the closed-loop system. The system matrices are assumed to depend polynomially on both the scheduling and uncertain parameters which are supposed to belong to intervals with a priori known bounds. To formulate the design problem in a linear matrix inequality (LMI) setting, a required auxiliary matrix is initially determined using a necessary condition for finding a gain-scheduled controller by the proposed method. Then, a robust gain-scheduled controller is designed by LMI conditions combined with a scalar search using the obtained auxiliary matrix. The method is applied to an inverted pendulum on a cart to illustrate the benefits and applicability of the proposed method.