Tutorial on Lyapunov-based methods for time-delay systems

Time-delay naturally appears in many control systems, and it is frequently a source of instability. However, for some systems, the presence of delay can have a stabilizing effect. Therefore, stability and control of time-delay systems is of theoretical and practical importance. Modern control systems usually employ digital technology for controller implementation, i.e. sampled-data control. A time-delay approach to sampled-data control, where the system is modeled as a continuous-time system with the delayed input/output became popular in the networked control systems, where the plant and the controller exchange data via communication network. In the present tutorial, introduction to Lyapunov-based methods for stability of time-delay systems is given together with some advanced results on the topic.