Section: New Results

$H_{\infty }$-stability analysis of neutral systems with commensurate delays

Participants : Catherine Bonnet, Le Ha Vy Nguyen.

We have analyzed [32] the $H_{\infty }$-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 $H_{\infty }$-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.