Robustly stabilizing controllers for dissipative infinite-dimensional systems with collocated actuators and sensors

We derive formulas for normalized doubly coprime factorizations over H"~ 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 @S(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.

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