A time delay exists between driver input and vehicle braking state response during the working process of the anti-lock braking system (ABS), and the braking performance of vehicles will be further reduced due to the delay of controllers. This paper investigates a systematic method of stability analysis for time delay ABS, and the analysis focuses on the stability and critical delay algorithm of ABS with delay time. Firstly, the dynamic structure and modelling process of ABS are briefly introduced, and PD control algorithm is adopted to improve the control performance. Then, dynamic models of ABS with time delay are derived, and the full delay stability interval and critical time delay algorithm of ABS are deduced by using the generalized Sturm criterion method. Finally, the validity of the critical delay algorithm by the proposed method and the stability and accuracy of ABS with time delay, different road conditions, vehicle speeds and control parameters are illustrated by numerical simulations, and the results show that the critical time delay algorithm of ABS can be verified under different conditions.
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