Stabilization of fractional neutral systems with one delay and a chain of poles asymptotic to the imaginary axis

International audienceIn this paper we consider the stabilizability of fractional single delay systems of the neutral type which have a chain of poles clustering the imaginary axis. These systems are H∞-stabilizable, however we prove here that the subclass of H∞-stabilizing controllers which are given in terms of polynomials in the Laplace variable s, sv and e-ST (where v is a rational, v ϵ (0,1) and τ real positive is the value of the delay) cannot move the chain of poles far away from the imaginary axis in the left half-plane as they necessarily introduce stable chains of poles clustering the imaginary axis in the closed-loop. Some examples and simulations are given