@article{Wang2025, 
author = {Yiyan Wang and Dongxia Zhao and Caifen Sun and Yaping Guo},
title = {Exponential stability of ARZ traffic flow model based on    2  ×  2 variable-coefficient hyperbolic system},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {1},
pages = {584-597},
keywords = {Lyapunov function, exponential stability, boundary feedback control, traffic flow model, variable-coefficient hyperbolic system},
url = {https://www.sciopen.com/article/10.3934/math.2025026},
doi = {10.3934/math.2025026},
abstract = {This paper studies the exponential stability of the Aw-Rascle-Zhang (ARZ) traffic flow model. Given that the steady state may be non-uniform, we obtain a    2  ×  2 hyperbolic system with variable coefficients. Then, by combining ramp metering and variable speed limit control, we deduce a kind of proportional boundary feedback controller. The well-posedness of the closed-loop system is proved by using the theory of semigroups of operators. Moreover, a novel Lyapunov function, whose weighted function is constructed by the solution of a first-order ordinary differential equation, can be used for the stability analysis. The analysis gives a sufficient stability condition for the feedback parameters, which is easy to verify. Finally, the effectiveness of boundary control and the feasibility of the feedback parameters are obtained by numerical simulation.}
}