We derive formulas for normalized doubly coprime factorizations over H-infinity for a class of nonexponentially stabilizable systems. Using these results, we solve the problem of robust stabilization with respect to normalized coprime factor perturbations for a class of infinite-dimensional systems Sigma(A, B, B*, D), with finite-rank inputs and outputs and dissipative operator A; these systems are not exponentially stabilizable. We give a parameterization of controllers that achieve a given robustness margin.