Feedback Stabilization of Linear Retarded Systems in Banach Spaces

Feedback stabilizability is studied for linear retarded systems in Banach spaces. Under the assumptions that the control is finite dimensional and the corresponding instantaneous free system generates a compact semigroup, the rank condition for exponential stabilizability is established based on the stabilizability result due to Bhat and Wonham. The condition is expressed in terms of eigenvectors and controllers, and the equivalent spectral mode controllability and observability conditions are given. An application is given to a class of parabolic partial functional differential equations with mixed boundary conditions