Section: New Results

Stabilization of fractional neutral systems with commensurate delays

Participants : Le Ha Vy Nguyen, Catherine Bonnet.

We consider fractional neutral systems with commensurate delays which may have chains of poles asymptotic to vertical lines lying in the open left half-plane and have chains clustering the imaginary axis. Due to the latter, the system may possess infinitely many poles in the right half-plane. We prove that a class of rational fractional controllers cannot stabilize this kind of systems in the sense of $H_{\infty }$ except in a simple case. For this case, thanks to the fractional PI controller given in [1] , a parametrization of stabilizing controllers is derived [105] .