Author Description

Time delay systems exist in many engineering?elds such as transportation, communication, process engineering and more recently networked control s- tems. In recent years, time delaysystems haveattracted recurring interests from research community. Much of the research work has been focused on stability analysis and stabilization of time delay systems using the so-called Lyapunov- Krasovskii functionals and linear matrix inequality (LMI) approach. While the LMI approach does provide an e?cient tool for handling systems with delays in state and/or inputs, the LMI based results are mostly only su?cient and only numerical solutions are available. For systems with knownsingle input delay, there have been rather elegant- alytical solutions to various problems such as optimal tracking, linear quadratic regulation and H control. We note that discrete-time systems with delays can? usually be converted into delay free systems via system augmentation, however, theaugmentationapproachleadsto muchhigher computationalcosts, especially for systems of higher state dimension and large delays. For continuous-time s- tems, time delayproblemscaninprinciple betreatedby thein?nite-dimensional system theory which, however, leads to solutions in terms of Riccati type partial di?erential equations or operator Riccati equations which are di?cult to und- stand and compute. Some attempts have been made in recent years to derive explicit and e?cient solutions for systems with input/output (i/o) delays. These include the study ontheH controlofsystemswith multiple input delaysbased? on the stable eigenspace of a Hamlitonian matrix [46].