Stability Analysis of Car-Following Systems With Uniformly Distributed Delays Using Frequency-Sweeping Approach

Abstract

In this paper, the stability problem of a class of deterministic car-following systems with uniformly distributed delays is addressed with a particular focus on the effects induced by the delay parameters on the stability. To perform such an analysis, the frequency-sweeping approach introduced recently by the authors will be adopted. The corresponding results are easy to derive and to implement. As a byproduct of the analysis, the complete characterization of the delay intervals guaranteeing stability is explicitly derived. Two case studies with different network topology types (linear and ring configurations) are studied in detail. The stability problem of car-following systems under consideration is a specific consensus problem of multi-agent systems. Such examples allow illustrating the approach as well as the positive effect of using uniformly distributed delay in the modeling (compared with the commonly-used pointwise delay). The derived results show that the approach is effective and may be adopted to more general consensus problems for multi-agent systems.

Keywords

• Car-following systems
• uniformly distributed delay systems (UDDSs)
• complete stability problem
• frequency-sweeping approach
• consensus of multi-agent systems