Introduction

Many things that happen around us can be called systems in view of causality. From centuries ago, we began to elucidate the phenomena that take place in these systems around us. There are several factors that have a decisive influence on the dynamic characteristics of the systems. Among such factors, an important element that exists anywhere in the world is the time delay. In the view of science history, the existence of this time lag since the 18th century has become known, and it has become clear that in many systems its existence cannot be absolutely negligible in dynamic properties. Since the industrial revolution of the nineteenth century, as the rapid development of various engineering including mechanical engineering, more accurate system analysis was required. Of course, it has already been shown that the dynamic effects of these time delays are also widespread in biological and sociological phenomena. Since the time delay may become long especially in the hardware and signal processing of the system, there is a big difference from the actual phenomenon when the system analysis is performed with the mathematical model ignoring the time delay. It is also found that when the system naturally has a time delay, the stability and performance of the system gradually deteriorates We also found that when the system naturally has a time delay, the stability and performance of the system gradually deteriorates as the magnitude of the delay increases.