Study on the Lyapunov Stability of a Time-Discrete Macro Traffic System with Variable Delay and Feedback Control

Abstract

This paper constructs and analyzes a time-discrete macro traffic system with bounded variable delay and feedback control strategy. By theoretical analysis using the Lyapunov theorem, a stable condition of the macro traffic system is derived under which traffic jams can be suppressed. The traffic developing properties of the new traffic system for different variable delay and feedback control parameters are illustrated through simulation. The results show that variable delay can easily lead a traffic system to evolve into a traffic jam, and the feedback control strategy can enhance the stability of the traffic system with respect to variable delay. Moreover, the traffic unstable level caused by variable delay is less than the unstable extent caused by the constant upper bound of variable delay; still it is more serious than the traffic fluctuation caused by the constant lower bound of variable delay.