Stability of distributed parameter systems with finite-dimensional controller-compensators using singular perturbations

Using a singular perturbation formulation of the linear time-invariant distributed parameter system, we develop a method to design finite-dimensional feedback compensators of any fixed order which will stabilize the infinite-dimensional distributed parameter system. The synthesis conditions are given entirely in terms of a finite-dimensional reduced-order model; the stability results depend on an infinite-dimensional version of the Klimushchev-Krasovskii lemma presented here.