Time-delays are important components of many dynamical systems that describe coupling or interconnection between dynamics, propagation, or transport phenomena in shared environments, in heredity, and in competition in population dynamics. This monograph addresses the problem of stability analysis and the stabilisation of dynamical systems subjected to time-delays. It presents a wide and self-contained panorama of analytical methods and computational algorithms using a unified eigenvalue-based approach illustrated by examples and applications in electrical and mechanical engineering, biology, and complex network analysis. This text bridges the fields of control (analysis and feedback design, robustness, and uncertainty) and numerical analysis (explicit algorithms, and methods). The authors provide an overall solution to the (robust) stability analysis and stabilisation problem of linear time-delay systems, which is the result of this cross-fertilisation of control theory, numerical linear algebra, numerical bifurcation analysis and optimisation.
Table of Contents
Preface; List of symbols; List of abbreviations; Part I. Stability Analysis of Linear Time-Delay Systems: 1. Spectral properties of linear time-delay systems; 2. Pseudospectra and robust stability analysis; 3. Computation of stability regions in parameter spaces; 4. Stability regions in delay-parameter spaces; 5. Delays ratio sensitivity and interference; 6. Stability of linear periodic systems with delays; Part II. Stabilization and Robust Stabilization: 7. The continuous pole placement method; 8. Stabilizability with delayed feedback: a numerical case-study; 9. The robust stabilization problem; 10. Stabilization using a direct eigenvalue optimization approach; Part III. Applications: 11. Output feedback stabilization: the single delay case; 12. Output feedback stabilization: the multiple delay case; 13. Congestion control algorithms in networks; 14. Smith predictor for stable systems: delay sensitivity analysis; 15. Controlling unstable systems using finite spectrum assignment; 16. Consensus problems in traffic flow applications; 17. Stability analysis of delay models in biosciences; A. Appendices; Bibliography; Index.
Wim Michiels is a Postdoctoral Fellow of the Fund for Scientific Research-Flanders at the Department of Computer Science of the K.U. Leuven. Silviu-Iulian Niculescu is the Research Director at CNRS L2S (Laboratory of Signals and Systems), Gif-sur-Yvette, France.