Section: New Results

Stability analysis of fractional and classical neutral systems with commensurate delays

Fractional and classical neutral systems with commensurate delays have chains of poles asymptotic to vertical lines (see [66] for classical systems). The delicate case where system have some chains of poles asymptotic to the imaginary axis is interesting as the absence of poles in the open left half-plane does not guarantee the $H_{\infty }$-stability of the system.

Stability analysis of classical or fractional neutral systems with one single chain of poles asymptotic to the imaginary axis has been investigated in [88] , [70] , [2] , [69] , where the asymptotic location of poles of neutral chains was given and necessary and sufficient conditions for $H_{\infty }$-stability were derived.

We have performed a full analysis of classical and fractional systems with multiple chains of poles approaching a set of points on the imaginary axis. Moreover, a unified method to analyze the stability of fractional and classical systems has been derived.