Feedback stabilization of abstract neutral linear control systems

In this paper, the asymptotic stabilization of linear distributed parameter control systems of neutral type is considered. Specifically, we study control systems described by a special type of abstract neutral functional differential equation with finite delay. Assuming appropriate conditions, and using the spectral properties of quasi-compact semigroups, we show that the usual spectral controllability assumption implies the feedback stabilization of the system. We applied our results to the stabilization of several real systems of first and second order described by partial neutral functional differential equations.