Robustness of Feedback Control Systems of Parabolic Type against Perturbations to an Elliptic Operator

We study robustness (stiffness) of feedback stabilization schemes for linear control systems of parabolic type against perturbations. The perturbations, often interpreted as modeling errors of physical systems, enter both the principal part and the boundary condition of the elliptic differential operator, which causes the change of the domain of definition for the elliptic operator. It is shown that the stabilization scheme works effectively for slightly perturbed systems insofar as the perturbations are small in adequate topologies. A study of various fractional powers of perturbed elliptic operators is the key to the theory. Made also is a characterization of domains of fractional powers of an elliptic operator with a feedback boundary condition.