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

Abstract— This paper is concerned with the problem of H∞ 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 2D H∞ 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∞ dynamic output feedback (DOF) control problem is considered by formulating it as a 2-D H∞ SOF control problem. A numerical example is provided to demonstrate the effectiveness and advantage of the proposed method.