Time-delay systems are a specific class of dynamic systems where the output at a given time is dependent not only on the current input but also on past inputs. These systems are prevalent in a wide range of fields such as engineering, biology, economics, and physics. The presence of time delays can lead to complex behavior such as oscillations, instability, and performance degradation. Researchers in this area focus on developing mathematical models, analysis techniques, and control strategies to understand and manage the effects of time delays in systems. Key challenges in this research area include dealing with the nonlinearity and uncertainty associated with time delays, as well as designing robust and efficient control algorithms to stabilize and optimize system performance.