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In practical application, the phenomenon of time delay inevitably exists in all kinds of systems. Although the time delay is small, it has a certain influence on the stability and control performance of the control system. In this paper, the rise and development of the time-delay dynamic vibration reduction theory are summarized. Since the time-delay vibration reduction technology was proposed, scholars have conducted a lot of theoretical research, and the research field has expanded from the linear system when it was first proposed to the nonlinear system, and achieved good research results. At present, the main research methods of linear or nonlinear ordinary differential equations with time delay can be divided into time domain method and frequency domain method. The dynamics research of this kind of system mainly focuses on stability analysis, perturbation technology, Holp bifurcation, chaos and so on. The research shows that both linear and nonlinear systems have good application value in vehicle engineering. By selecting reasonable time-delay control parameters, the vehicle body vibration can be greatly suppressed.

A Brief Discussion on the Research Progress of the Theory of Dynamic Vibration Reduction with Time Delay