Robustly stabilizing controllers with respect to left-coprime factor perturbations for infinite-dimensional linear systems

We solve the problem of robust stabilization with respect to left-coprime factor perturbations for a large class of irrational transfer functions with a realization in terms of unbounded operators. The key condition is that the associated dynamical system and its dual should satisfy a finite-cost condition so that two optimal cost operators exist. We obtain an explicit parameterization of infinitely many robustly stabilizing controllers in terms of these optimal cost operators and the generating operators of the realization.