High-order analysis of critical stability properties of linear time-delay systems

Peilin Fu (1) , Jie Chen (1) , Silviu-Iulian Niculescu (2)

1 UC Riverside - University of California [Riverside]
2 L2S - Laboratoire des signaux et systèmes

In this paper we study stability properties of linear time-delay systems with commensurate delays. We investigate specifically the asymptotic behavior of the critical characteristic zeros of time-delay systems on the imaginary axis. This behavior determines whether the imaginary zeros cross from one half plane into another, and hence plays a critical role in determining the stability of a time-delay system. We emphasize in particular the second-order asymptotic properties, which, together with earlier results on first-order analysis, provide a more complete characterization of the zero asymptotic behavior.

Mots clés: time-delay; asymptotic stability; critical zeros; asymptotic behavior; matrix pencil

Domaines: Automatique

Peilin Fu, Jie Chen, Silviu-Iulian Niculescu. High-order analysis of critical stability properties of linear time-delay systems. 26th American Control Conference, Jul 2007, New York, NY, United States. ⟨hal-02194454⟩