A note on stability and stabilizability of neutral systems

This note presents frequency-domain characterizations of exponential stability and stabilizability of neutral systems based on transfer-function matrices and the existence of `nice´ solutions of certain Bezout equations. It turns out that the existence of H^∞-solutions is not sufficient for exponential stabilizability, but that they have to satisfy an additional growth assumption as well. Whilst the proofs of the authors´ results are based on an abstract infinite-dimensional representation of the neutral system, they emphasize that the results are expressed in terms of the original parameters of the neutral equation and do not require a reformulation of the system in an abstract state-space form. The sufficiency parts of the results hold even when the delay operator acting on the derivative contains a singular part