Time-delays are important components of many dynamical systems that describe coupling or interconnection between dynamics, propagation or transport phenomena, and heredity and competition in population dynamics. This monograph addresses the problem of stability analysis and the stabilization 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 present solutions of the (robust) stability analysis and stabilization problem of linear time-delay systems, which are the result of this cross-fertilization of control theory, numerical linear algebra, numerical bifurcation analysis, and optimization.
The book is organized into three parts: Part I addresses the analysis of linear time-delay systems from a stability point of view. Part II is devoted to synthesis problems with the focus on stabilization. In Part III the authors present a wide class of applications, including congestion analysis in high-performance networks, output feedback stabilization using the delays as controller parameters, predictor-type controllers, consensus problems in traffic flows, and stability analysis of various delay models in the biosciences.
Audience: Researchers and graduate students in electrical and mechanical engineering, computer science, biology, and applied mathematics will benefit from this book.
Contents: Preface; Symbols; Acronyms; Part I: Stability analysis of linear time-delay systems. Chapter 1: Spectral properties of linear time-delay systems; Chapter 2: Pseudospectra and robust stability analysis; Chapter 3: Computation of stability regions in parameter spaces; Chapter 4: Stability regions in delay-parameter spaces; Chapter 5: Delays ratio sensitivity and delay-interference; Chapter 6: Stability of linear periodic systems with delays; Part II: Stabilization and robust stabilization; Chapter 7: The continuous pole placement method; Chapter 8: Stabilizability with delayed feedback: a numerical case-study; Chapter 9: The robust stabilization problem; Chapter 10: Stabilization using a direct eigenvalue optimization approach; Part III: Applications. Chapter 11: Output feedback stabilization using delays as control parameters: the single delay case; Chapter 12: Output feedback stabilization using delays as control parameters: the multiple delay case; Chapter 13: Congestion control in networks; Chapter 14: Smith predictor for stable systems: delay sensitivity analysis; Chapter 15: Controlling unstable systems using finite spectrum assignment; Chapter 16: Consensus problems with distributed delays, with traffic flow applications; Chapter 17: Stability analysis of delay models in biosciences; Appendix; Bibliography; Index.