Robust stabilization of normalized coprime factors: an explicit H∞ solution

The problem of robustly stabilizing a linear system subject to H ∞ bounded perturbations in the Numerator, N, and denominator, M, of its normalized left coprime factorization is explicitly solved. Although this is a particular H ∞ optimization problem which would normally require an iterative solution, it can in fact be solved directly giving the optimal stability margin 1 - ||M , N|| 2 H .