H∞-stability analysis of various classes of neutral systems with commensurate delays and with chains of poles approaching the imaginary axis

We analyze the H_∞-stability of neutral systems with commensurate delays and multiple chains of poles asymptotic to a same set of points on the imaginary axis. First, by approximation, the location of poles of large modulus is determined. This analysis requires to consider several subclasses of systems where poles of high modulus exhibit various patterns. Second, we derive necessary and sufficient conditions for H_∞-stability which are easy to check as expressed in terms of the degrees of the polynomials involved in the numerator and denominator of the transfer function.