Pole assignment for distributed systems by finite-dimensional control

The question of pole assignment for a class of distributed systems by means of finite dimensional control is considered. A finite dimensional compensator is usually designed based on a reduced order model, and it is not a priori known what effect this will have on the original infinite dimensional system. Explicit formulas are derived which enable one to calculate the eigenvalues of the resulting closed loop system. For a certain compensator design, estimates are derived which can be used to guarantee stability a priori. Numerical results are also presented.