H<inf>∞</inf> static output feedback controller design for two-dimensional discrete systems in Roesser model

Abstract

This paper is concerned with the problem of H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> static output feedback (SOF) control of two-dimensional (2-D) discrete systems described by the Roesser model. By applying the 2-D Bounded Real Lemma, a design criterion for the 2-D H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> SOF controller is derived. Since the existence condition for the SOF controller is not expressed strictly in terms of linear matrix inequalities (LMIs), then an iterative algorithm is proposed to solve this nonconvex problem. Furthermore, the 2-D H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> dynamic output feedback (DOF) control problem is considered by formulating it as a 2-D H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> SOF control problem. A numerical example is provided to demonstrate the effectiveness and advantage of the proposed method.