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

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.