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 Lyapunovbased methods for stability of time-delay systems is given together with some advanced results on the topic. & 2014 European Control Association. Published by Elsevier Ltd. All rights reserved.