From 17/03 till 21/03 2025, a course on time-delay systems will be offered by the International Graduate School on Control of the European Embedded Control Institute (EECI). It will take place on the campus of the Université Paris-Saclay at Gif-sur-Yvette, France. This will be the sixth time this course is organized (last edition in 2022), with updated contents and course material. Note that in most universities, the courses offered EECI can taken up as part of the formal PhD training.
Registration is via the website http://www.eeci-igsc.eu/
Abstract
The aim of this course is to describe fundamental properties of systems including time-delays in their representation, 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 teleoperation to communication networks, from biological systems to population dynamics and genetic regulatory networks) complete the presentation. In particular, the synergies of analytic and computational tools for analysis and design are highlighted. The course is complemented with home-works where analysis and control design problems are solved using dedicated software tools.
More precisely, the following aspects are covered:
Theory:
- Classification and representation
- Definition and properties of solutions of delay systems
- Spectral properties of linear time-delay systems
Analysis:
- Frequency-domain approaches
- Stability domains in parameter spaces
- Relative stability and synchronization
- Robustness and performance measures
- Time-domain, Lyapunov based criteria, Lyapunov matrices and converse theorems
Control design:
- Fundamental limitations of delays in control loops
- Structured stabilizing and optimal H-2 and H-infinity controllers (fixed-order, PID, decentralized,…)
- Delay compensation using predictor and periodic feedback
- Improving stability and performance by using delays as control parameters
