Stability, Control, and Computation for Time-Delay Systems (2^nd Ed.) An Eigenvalue-Based Approach

Time delays are important components of dynamical systems, whether in engineering, physics, economics, or the life sciences. Through a unifying eigenvalue-based framework, this monograph presents an overall solution to stability analysis, stabilization, and the robust fixed-order control problem for time-delay systems. The authors offer a range of both analytical methods and numerical algorithms, applicable to a broad class of linear time-delay systems that includes retarded- as well as neutral-type systems. Integrating leading-edge research from control theory, optimization, numerical linear algebra and bifurcation analysis, this book has high relevance across systems and control theory, computer science, applied mathematics and computational mathematics alike. New to this edition is the inclusion of both retarded-type and neutral-type systems; a broader scope of solution includes not only stabilization but the design of robust and optimal controllers; while an increased range of applications from electrical engineering to biology showcases the effectiveness and generality of the solution more effectively.

Preface to the second edition; Preface to the first edition; List of symbols; Acronyms; Part I. Stability Analysis of Linear Time-Delay Systems; 1. Spectral properties of linear time-delay systems; 2. Computation of characteristic roots; 3. Pseudospectra and robust stability analysis; 4. Computation of H2 and H∞ norms; 5. Computation of stability regions in parameter spaces; 6. Stability regions in delay-parameter spaces; Part II. Stabilization and Robust Fixed-Order Control: 7. Stabilization using a direct eigenvalue optimization approach; 8. Stabilizability with delayed feedback: a numerical case study; 9. Optimization of H∞ norms; Part III. Applications: 10. Output feedback stabilization using delays as control parameters; 11. Smith predictor for stable systems: delay sensitivity analysis; 12. Controlling unstable systems using finite spectrum assignment; 13. Congestion control algorithms in networks; 14. Consensus problems with distributed delays, with traffic flow applications; 15. Synchronization of delay-coupled oscillators; 16. Stability analysis of delay models in biosciences; Appendix; Bibliography; Index.

Wim Michiels is an associate professor at KU Leuven, where he leads a research team within the Numerical Analysis and Applied Mathematics Division. He has coauthored more than 75 journal papers in the areas of control and optimization and computational and applied mathematics, coauthored the monograph Stability and Stabilization of Time‐Delay Systems: An Eigenvalue-Based Approach (SIAM, 2007), and coedited three other books.
Silviu-Iulian Niculescu is senior researcher at CNRS at the Laboratory of Signals and Systems (L2S), CNRS-Supélec, Gif-sur-Yvette, France. In 2006 he joined the L2S, which he has headed since January 2010. He is the coauthor of more than 400 book chapters, journal papers, and communications in international conferences, has coauthored five books, and is coeditor of six multiauthor volumes.