A Simple Unified Formula for Discrete and Continuous-time H∞ “All-solutions” Controllers

In this paper we present a simple, unified formula for discrete and continuous-time H∞ “all-solutions” controllers. By observing a “cost” equivalence between the standard H∞ control problem and a certain LQ optimal regulator problem, an elegant controller structure reminiscent of an LQG optimal controller is developed. Our choice of notation also simplifies the derivation and existence conditions considerably, whereby all unnecessary assumptions on plant state-space matrices and “loop-shifting” transformations are eliminated. Additionally, with our focus entirely on input-output weighting “cost functions” this derivation offers a “behavioral” theory interpretation for all solutions of a standard H∞ control problem.