Stabilization strategies of a general nonlinear car-following model with varying reaction-time delay of the drivers

•The reaction-time delay of the drivers in car-following model is time varying.•The stability strategy for the car-following model is given.•The robust state feedback control strategy is designed.•The proposed methods can effectively suppress the traffic jam.

In this paper, the stabilization strategies of a general nonlinear car-following model with reaction-time delay of the drivers are investigated. The reaction-time delay of the driver is time varying and bounded. By using the Lyapunov stability theory, the sufficient condition for the existence of the state feedback control strategy for the stability of the car-following model is given in the form of linear matrix inequality, under which the traffic jam can be well suppressed with respect to the varying reaction-time delay. Moreover, by considering the external disturbance for the running cars, the robust state feedback control strategy is designed, which ensures robust stability and a smaller prescribed H∞ disturbance attenuation level for the traffic flow. Numerical examples are given to illustrate the effectiveness of the proposed methods.