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/sup /spl infin//-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.<
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