Optimization of Coordinate Transformation Matrix for H∞ Static-Output-Feedback Control of Linear Discrete-Time Systems

This paper presents a new iterative algorithm as an upgrade to sufficient LMI conditions for the H∞ static‐output‐feedback (SOF) control of discrete‐time systems. Based on an analysis of the structures of the coordinate transformation matrix and the Lyapunov matrix, the open question of how to fix the Lyapunov matrix structure raised by G. I. Bara and M. Boutayeb is replaced with the question of how to choose the coordinate transformation matrix. Then, an iterative algorithm for selecting the optimum coordinate transformation matrix that produces a locally optimal solution is presented. Finally, numerical examples demonstrate the effectiveness and advantages of this method.