Abstract
A discrete-time car-following model with consideration of stable velocity control strategy is introduced and analyzed in this paper. By using the discrete-time Lyapunov stability theorem, a sufficient stable condition of the new model is derived and given in the form of linear matrix inequality. Through numerical simulation, the traffic flow evolution rules of the new model with stable velocity control strategy or not are exhibited. The results show that the unstable traffic flow is consistent to the stop-and-go density wave in real traffic. Also, traffic congestion of the new model with stable velocity control strategy can be suppressed comparing to the case without control. It is revealed that the stable velocity control strategy should be considered in real traffic to enhancing traffic stability.
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