ABSTRACT
Time-delay systems (TDS) are also called systems with aftereffect or dead-time, hereditary systems, equations with deviating argument, or differential-difference equations. They belong to the class of functional differential equations that are infinite-dimensional, as opposed to ordinary differential equations. In spite of their complexity, TDS often appear as simple infinite-dimensional models of more complicated partial differential equations. Time-delay often appears in many control systems either in the state, the control input, or the measurements. There can be transport, communication, or measurement delays. Actuators, sensors, and field networks that are involved in feedback loops usually introduce delays. Thus, delays are strongly involved in challenging areas of communication and information technologies: stability of networked control systems or high-speed communication networks. Delays are known to have complex effects on stability: they may be a source of instability. As in systems without delay, an efficient method for stability analysis of TDS is the direct Lyapunov method.
