Robustly Stabilizing Controllers with Internal Loop

Abstract

The problem of robust stabilization with respect to left coprime factor perturbations was first solved explicity for the rational case in Glover and McFarlane [14]. The irrational case was treated in Georgiou and Smith [12], where it was shown that a solution exists provided that the transfer function has a normalized doubly coprime factorization. Our new contribution is to solve this classic problem for the following very general class of transfer functions $\mathbf{G}(s)\in\mathcal{L}(U,Y)$, where U, and Y are separable Hilbert spaces and G has the following realization.