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Section: New Results

Stabilization of fractional neutral systems with commensurate delays

We consider strictly proper fractional neutral systems with one delay and one chain of poles asymptotic to the imaginary axis including the case where this chain may approach the axis from the right side. Thus the system may possess infinitely many poles in the right half-plane. For these systems, a Youla-Kučera parametrization regarding $H_{\infty }$-stability of all stabilizing controllers has been obtained in [59] . Having in mind the robustness of the closed-loop relative to parameter uncertainties, we wish to find controllers which are able to provide a closed-loop free of chain of poles asymptotic to the imaginary axis. However, we prove that a large class of realizable stabilizing controllers cannot achieve this. [47] .