Stabilization and a class of functionals for linear parabolic systems

We study in this paper stabilization by means of feedback control for a class of linear parabolic control systems and a related problem. The purpose of the paper is to construct a specific feedback control system such that the state decays exponentially with the designated decay rate, and that some nontrivial linear functionals of the state decay faster than the state. In particular, we extend the well known finite-dimensional pole assignment theory by W. M. Wonham (1967). Actually we derive the necessary and sufficient condition for an arbitrary allocation of the eigenvalues of coefficient matrices in linear feedback control systems which is subject to constraint.