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Journal Articles SIAM Journal on Control and Optimization Year : 2009

Consensus problems with distributed delays, with application to traffic flow models

Abstract

This paper focuses on consensus problems for a class of linear systems with distributed delay that are encountered in modeling traffic flow dynamics. In the application problems the distributed delay, whose kernel is 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 gamma-distribution kernel is developed. Also explicit expressions for the consensus function(al) of time-delay systems with constant and distributed delays that solve a consensus problem are provided. Several illustrative examples complete the presentation.

Dates and versions

hal-02195943 , version 1 (26-07-2019)

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Wim Michiels, Irinel-Constantin Morarescu, Silviu-Iulian Niculescu. Consensus problems with distributed delays, with application to traffic flow models. SIAM Journal on Control and Optimization, 2009, 48 (1), pp.77-101. ⟨10.1137/060671425⟩. ⟨hal-02195943⟩
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