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Stability and Stabilization of Time-Delay Systems: An Eigenvalue-Based ApproachStability and Stabilization of Time-Delay Systems: An Eigenvalue-Based Approach

Wim Michiels and Silviu-Iulian Niculescu

Advances in Design and Control 12

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.

Researchers and graduate students in electrical and mechanical engineering, computer science, biology, and applied mathematics will benefit from this book.

Table of Contents

Keywords: delay, stability, stabilization, eigenvalue analysis, dynamical systems

About the Authors
Wim Michiels is a Postdoctoral Fellow of the Fund for Scientific Research-Flanders at the Department of Computer Science of K.U.Leuven. Among other works, he is the author of over 30 articles in international journals and has edited Time-Delay Systems 2004 (Elsevier Science, 2005). His research interests include control and optimization, dynamical systems, numerical linear algebra, and scientific computing. His research has focused on the analysis and control of systems described by functional differential equations, with applications to problems from engineering and life sciences.

Silviu-Iulian Niculescu is a CNRS Senior Researcher at L2S (Laboratory of Signals and Systems), Gif-sur-Yvette, France. He is the author of Delay Systems: Qualitative Aspects on the Stability and Stabilization (Diderot, 1997) and Delay Effects on Stability: A Robust Control Approach (Springer, 2001). He has also written more than 225 book chapters or scientific papers and is the co-editor of four volumes. His research interests include delay systems, robust control, operator theory, and numerical methods in optimization and their applications to the design of engineering systems.

2007 / xxii + 378 pages / Softcover / ISBN 978-0-898716-32-0
List Price $105.50 / SIAM Member Price $73.85 / Order Code DC12

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