Relationship between discrete polynomial and state-space solutions of the H∞ optimal regulator problem

Abstract

A relationship is established between the discrete state-space and polynomial matrix solutions of the H∞ state-feedback sub-optimal regulator problem. The solution of polynomial matrix diophantine equations is related to the solution of the discrete H ∞ Riccati equation. The links between DGKF state-space and the polynomial system solutions provide insights into the structure of the controller that may be helpful for calculations and implementation.