On exponential stabilizability of linear neutral systems

In this paper, we deal with linear neutral functional differential systems. Using an extended state space and an extended control operator, we transfo rm the initial neutral system in an infinite dimensional linear system. We give a sufficient condition for admissibility of the control operator B, co nditions under which operator B can be acceptable in order to work with con trollability and stabilizability. Necessary and sufficient conditions for e xact controllability are provided; in terms of a gramian of controllability N(mu) Assuming admissibility and exact controllability, a feedback control law is defined from the inverse of the operator N(mu) in order to stabiliz e exponentially the closed loop system. In this case, the semigroup generat ed by the closed loop system has an arbitrary decay rare.