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].
