Robustly stabilizing controllers for strongly stabilizable and detectable infinite-dimensional systems

We solve the problem of robust stabilization with respect to normalized coprime factor perturbations for a class of infinite-dimensional systems with finite-rank, which are strongly stabilizable and detectable, but not exponentially stabilizable or detectable. The class includes dissipative distributed parameter systems with collocated actuators and sensors and in addition, certain hybrid flexible structure models with non-collocated sensors and actuators. Such systems typically have infinitely many unstable eigenvalues close to the imaginary axis.