On Pole Assignment and Stabilization for the Heat Equation

Abstract

For one type of infinite dimensional linear systems, specifically the heat equation, the possibility of assigning the infinite set of poles of a closed loop system formed by means of a suitable linear state feedback operator is discussed. Necessary and sufficient conditions are derived for the existence of a feedback opeartor to shift all the eigenvalues of the controllable system, and to assign an arbitrary finite set of poles of the closed loop system. As an application of this result, it is shown that an open loop controllable system can be stabilized in a desired order of convergence by a suitable choice of the feedback operator.