Consensus problems for car following systems with distributed delays

Wim Michiels (1) , Irinel-Constantin Morarescu (2, 3) , Silviu-Iulian Niculescu (4, 5)

1 KU Leuven - Catholic University of Leuven = Katholieke Universiteit Leuven
2 UTC - Université de Technologie de Compiègne
3 UPB - University Politehnica of Bucharest [Romania]
4 L2S - Laboratoire des signaux et systèmes
5 Heudiasyc - Heuristique et Diagnostic des Systèmes Complexes [Compiègne]

This paper focuses on consensus problems for a class of linear systems with distributed delay that are encountered in modeling traffic flow dynamics. The distributed delay, whose kernel is a gamma-distribution with a gap, represents the human drivers' behavior in the average. The aim of the paper is to give a characterization of the regions in the corresponding delay parameter space, where a consensus is reached for all initial conditions. The structure and properties of the system are fully exploited, which leads to explicit and computationally tractable expressions. As a by-product a stability theory for distributed delay systems with a gamma-distribution kernel is developed. Several illustrative examples complete the presentation. © 2007 EUCA.

Mots clés: Stability; traffic model; consensus problem; time-delays; sta- bility

Domaines: Informatique [cs]

Wim Michiels, Irinel-Constantin Morarescu, Silviu-Iulian Niculescu. Consensus problems for car following systems with distributed delays. 2007 9th European Control Conference, ECC 2007, Jul 2007, kos, Greece. pp.2158-2165, ⟨10.23919/ecc.2007.7068788⟩. ⟨hal-02272378⟩