State space formulae for stable rational matrix solutions of a Leech problem

Abstract

Given stable rational matrix functions G and K, a procedure is presented to compute a stable rational matrix solution X to the Leech problem associated with G and K, that is, G(z)X(z) = K(z) and sup|z|≤1 ∥X(z)∥ ≤ 1. The solution is given in the form of a state space realization, where the matrices involved in this realization are computed from state space realizations of the data functions G and K.