Two-Riccati formulae for the discrete-time H^∞ -control problem

Abstract

A two-Riccati state-space approach to the discrete-time H∞ control problem is presented. The main theoretical tool is the Kalman-Szego-Popov-Yakubovich system written in adequate forms in order to reduce the problems to a standard form for which the solutions are easily obtained. The necessity part of our main results uses a 'signed' counterpart of the positivity theorem.