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## Section: New Results

### Stability analysis of fractional neutral systems with commensurate delays

Participants : Le Ha Vy Nguyen, Catherine Bonnet.

Fractional neutral systems with commensurate delays have chains of poles aymptotic to vertical lines. The case where the imaginary axis is an asymptotic one is interesting. Indeed, if the system has some chains of poles asymptotic to the imaginary axis, then the fact that all poles lie in the open left half-plane does not guarantee the ${H}_{\infty }$-stability of the system.

This kind of systems was studied in [97] , [104] . In [97] , systems with single chains of poles asymptotic to the imaginary axis was considered and necessary and sufficient conditions for ${H}_{\infty }$-stability were derived. Some particular systems with multiple chains have been examined in [104] . We have extended this year this study to more general systems with multiple chains of poles approaching the imaginary axis.