Over one Century of Spectrum Analysis in Delay Systems: An Overview and New Trends in Pole Placement Methods

Amina Benarab (1, 2, 3) , Islam Boussaada (2, 3) , Silviu-Iulian Niculescu (1, 3) , Karim Trabelsi (2)

1 L2S - Laboratoire des signaux et systèmes
2 IPSA - Institut Polytechnique des Sciences Avancées
3 DISCO - Dynamical Interconnected Systems in COmplex Environments

Pole placement represents a classical method for controlling finite-dimensional linear timeinvariant systems, largely covered in the open literature. Basically, it consists of placing the poles of the closed-loop system in some predetermined loci in the complex plane. This paper discusses some of the extensions of this method to linear systems described by delay-differential equations. Among others, the finite spectrum assignment (FSA), the continuous pole placement (CPP) and the partial pole placement (PPP) approaches are presented and illustrated through some simple low-order dynamical systems.

Mots clés: Delay; Stability; Pole placement; Pole assignment

Domaines: Mathématiques [math]; Automatique / Robotique; Mathématiques générales [math.GM]; Science non linéaire [physics]; Systèmes et contrôle [cs.SY]

Amina Benarab, Islam Boussaada, Silviu-Iulian Niculescu, Karim Trabelsi. Over one Century of Spectrum Analysis in Delay Systems: An Overview and New Trends in Pole Placement Methods. TDS 2022 - 17th IFAC Workshop on Time Delay Systems, Sep 2022, Montreal, Canada. ⟨10.1016/j.ifacol.2022.11.363⟩. ⟨hal-03765146⟩