On exponential stabilizability of linear neutral systems

International audienceIn this paper, we deal with linear neutral functional differential systems. Using an extended state space and an extended control operator, we transform the initial neutral system in an infinite dimensional linear system. We give a sufficient condition for admissibility of the control operator $B$, conditions under which operator $B$ can be acceptable in order to work with controllability and stabilizability. Necessary and sufficient conditions for exact 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 stabilize exponentially the closed loop system. In this case, the semigroup generated by the closed loop system has an arbitrary decay rate