Robust \(H^ \infty\) disturbance minimization by duality (Q1199845)

In this very important paper the authors study the \(H^ \infty\) optimization problem \[ \inf_{Q\in H^ \infty} \|| W(1- PQ)|+| VPQ|\|_ \infty,\tag{1} \] where \(P\in H^ \infty\) is a plant, \(W\), \(V\) are weighting functions. It is shown that this problem is in a sense equivalent to a best approximation problem in a Banach space. Duality methods are used to investigate the latter problem. It is shown that the solution of (1) is allpass and, in the single-input- single-output case, unique.