<i><scp>H</scp>_∞</i> Static Output Feedback Control of 2‐<scp>D</scp> Discrete Systems in <scp>FM</scp> Second Model

Abstract

Abstract The problem of H ∞ static output feedback ( SOF ) control of two‐dimensional (2‐ D ) discrete systems described by the F ornasini‐ M archesini ( FM ) second model is investigated in this paper. First, by applying the 2‐ D B ounded R eal L emma, the 2‐ D H ∞ SOF control problem is formulated in terms of a bilinear matrix inequality ( BMI ). Then, by combining the slack variable technique with two kinds of existing LMI methods, respectively, less conservative sufficient LMI conditions are proposed for the BMI formulation. The relation of these two kinds of LMI conditions are revealed by analyzing the choices of coordinate transformation matrices involved in the first kind of LMI conditions. Finally, a numerical example is provided to demonstrate the effectiveness and merits of the proposed methods.