ON THE DISCRETE-TIME BOUNDED REAL LEMMA WITH APPLICATION IN THE CHARACTERIZATION OF STATIC STATE FEEDBACK H-INFINITY CONTROLLERS

This paper deals with the Discrete-time Bounded Real Lemma and its application in the characterization of all static state feedback H infinity controllers for discrete-time systems. We first present two versions of the Discrete-time Bounded Real Lemma. The results apply to non-minimal stable state-space realizations and are given in terms of either the positive semi-definite strong solution, or the positive semi-definite stabilizing solution of a discrete algebraic Riccati equation. Based on the Discrete-time Bounded Real Lemma, we obtain a characterization of all static state feedback H infinity controllers for discrete-time systems. As an application of the parameterization of all static state feedback H infinity controllers, we develop a solution to the discrete-time H infinity control problem via static output feedback. Also, a numerical procedure is proposed to determine an output feedback gain.