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
.