M11 – PARIS‐SACLAY 14/03/2016 ‐ 18/03/2016

Stability, Control, and Computation for Time-delay Systems

Wim Michiels
Department of Computer Science
KU Leuven, Belgium
     Silviu-Iulian Niculescu
     Laboratoire des Signaux et Systèmes (L2S)
     CNRS-CentraleSupélec-U PSUD, France

Abstract of the course

The aim of this course is to describe fundamental properties of systems subjected to time-delays and to present an overview of methods and techniques for the analysis and control design. The focus lies on systems described by functional differential equations and on frequency domain techniques, grounded in numerical linear algebra (e.g., eigenvalue computations) and optimization, but the main principles behind time-domain methods are addressed as well. Several examples (from chemical to mechanical engineering, from haptics systems and tele-operation to communication networks, from biological systems to population dynamics and genetic regulatory networks) complete the presentation. The course is complemented with home-works where control design problems are solved using recently developed software.


 Classification and representation
Definition and properties of solutions  of delay
• Spectral properties of linear time-delay systems

Stability using time and frequency domain methods
Stability domains in parameter spaces
Robustness and performance measures

Control design:
Fundamental limitations of delays in control loops
Fixed-order stabilizing and optimal  H-2 and H-infinity controllers
Prediction based controllers
Using delays as controller parameters