Geometric vs. algebraic approach: A study of double imaginary characteristic roots in time-delay systems

Dina Irofti (1) , Islam Boussaada (1) , Silviu-Iulian Niculescu (1, 2)

1 L2S - Laboratoire des signaux et systèmes
2 DISCO - Dynamical Interconnected Systems in COmplex Environments

This paper studies double imaginary characteristic roots in the case of time-delay systems with two delays as parameters. We aim to identify the direction in which double roots cross the imaginary axis, when the delay parameters change. To determine what happens when parameters are under a small perturbation, we present two methods: the algebraic and geometric approaches. Taking a theoretical example, we show that, even if the two methods are conceptually different, the provided results are consistent.

Keywords: Characteristic roots; Spectral analysis; Time delay; Stability analysis; Distributed Parameter Systems

Domains: Automatic

Dina Irofti, Islam Boussaada, Silviu-Iulian Niculescu. Geometric vs. algebraic approach: A study of double imaginary characteristic roots in time-delay systems. IFAC 2017 - 20th World Congress of the International Federation of Automatic Control, Jul 2017, Toulouse, France. pp.1310 - 1315, ⟨10.1016/j.ifacol.2017.08.123⟩. ⟨hal-01815469⟩