Workshop Proposal (IEEE CDC 2009):
Stability and Control of Time-Delay Systems
Summary:
This workshop will present an up-to-date tutorial of the stability analysis and control of time-delay systems
as well as various applications with a particular attention devoted to traffic flow models. The time-delay is a wellknown
component in many dynamical systems, which may arise, e.g., as an intrinsic part of the system, through input
and measurement channels of feedback, or as a result of simplification from partial differential equations. Process
control (as assumed in the classical Ziegler-Nichols PID control tuning rule) and chaos control are two examples
among numerous practical applications spanning biology, ecology, economy, and of course, engineering.
In this tutorial workshop, after a brief introduction on the problem set up and some classical results, the emphasis
will be placed on recent research achievements on the stability and control results, as well as their applications.
In frequency-domain, the introductory talks focus on the stability of linear systems including multiple delays, and
more precisely, on the computation of the critical roots on the imaginary axis as well as of the crossing direction
with respect to the delay parameters. The methods considered are: the eigenvalue-based approach and the Rekasius
transformation. Next, the geometric characterization of the stability regions in appropriate parameter-spaces
is presented with some standard control problem, as for example, the PI and PID control or the delay sensitivity
mechanisms for Smith predictors are readdressed in such a perspective. This frequency-domain part ends by the
application of the eigenvalue approach to the design of feedback controllers. The third part will be devoted to timedomain
methods and in particular the Lyapunov theory. More precisely, simple Lyapunov functionals, and complete
Lyapunov-Krasovskii functionals (LKF) are introduced and discussed. A particular attention will be paid to the
construction of LKF for dynamical systems described by coupled delay-difference and delay-differential equations
encountered in various physical models describing propagation and transport phenomena. Finally, the last part will
be devoted to the application of these stability and control results to models of traffic flow and in particular to car
following systems.
Organizers: Silviu-Iulian NICULESCU (France), Keqin GU (USA) & Jie CHEN (USA)
Place: Shanghai (PR China)
Date: December 15th, 2009