Robust Stabilization of Infinite-Dimensional Systems with Respect to Coprime Factor Perturbations

This paper solves the problem of robust stabilization of a class of infinite-dimensional systems with respect to stable factor perturbations of a fixed normalized left-coprime factorization. The class of infinite-dimensional systems is that described by the state-space operators (A, B,C,D) where A generates a strongly continuous semigroup on Hilbert spaces V and W, D(A^V ) ↪ W ↪ V and the system has a bounded observability map from V and a bounded controllability map onto W (the Prit chard-S alamon class). C ϵ ℒ(W,Y) and Β ϵ ℒ(V, U), where U and Y are separable Hilbert spaces and in addition, we assume that (A, B) is admissibly exponentially stabilizable, (A, C) is admissibly exponentially detectable.