A unified model for general delay systems

In the paper, we discuss the unifying modeling of a general class of equivalent time delay systems. A unified model in the form of coupled differential difference equations (CDDEs) for general delay systems is proposed by using the “pull out delays” method in the modeling process. And then its equivalence to other CDDEs is proven in a systematic manner. Generality of the unified model is clarified including as special cases many classes of delay systems, such as retarded, neutral, singular delay systems and so forth. Lastly, possible extensions of the established results in several ways are pointed out in the conclusion.