Robustness and continuity of the spectrum for uncertain distributed parameter systems

Abstract

We analyze the spectrum of a class of abstract partial differential equations with boundary feedback control. If we interpret the feedback as a perturbation then we obtain a robustness radius for spectrum placement. We obtain continuity of the spectrum using this radius and Rouche's theorem. We exploit extensively recent developments in the representation theory for abstract linear systems, especially regular systems. We also analyze ill-posed systems by interchanging the roles of input and output. We apply these results to a wave equation and an ill-posed beam equation.