Simultaneous design of robust gain‐scheduled static output‐feedback controller and scaling matrices for linear parameter varying systems with inexact scheduling parameters

Abstract

This article presents a design method of the robust gain‐scheduled static output‐feedback controller exploiting inexact measured scheduling parameters for multi‐affine linear parameter‐varying systems with structured uncertainty blocks. Performance scaling matrices are introduced in the design process to reduce conservatism. By introducing auxiliary variables and properly utilizing projection lemma, a parameter‐dependent linear matrix inequality with a single line search parameter is derived to synthesize the static output‐feedback controller gains and scaling matrices simultaneously. Based on vertices of the convex polytope covering the admissible region of scheduling parameters and inexact ones, the given parameter‐dependent synthesis condition is further expressed as a set of linear matrix inequalities at the vertices of the polytope to guarantee the robustness against inaccurate scheduling parameters. Several examples show the effectiveness of the proposed algorithm.