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

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  • Format: Paperback
  • Copyright: 2007-10-25
  • Publisher: Society for Industrial & Applied

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Supplemental Materials

What is included with this book?


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.

Author Biography

Wim Michiels is a Postdoctoral Fellow of the Fund for Scientific Research-Flanders at the Department of Computer Science of K.U.Leuven. He is the author of, among other published works, 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.

Table of Contents

List of symbols
List of abbreviations
Stability Analysis of Linear Time-Delay Systems:
Spectral properties of linear time-delay systems
Pseudospectra and robust stability analysis
Computation of stability regions in parameter spaces
Stability regions in delay-parameter spaces
Delays ratio sensitivity and interference
Stability of linear periodic systems with delays
Stabilization and Robust Stabilization:
The continuous pole placement method
Stabilizability with delayed feedback: a numerical case-study
The robust stabilization problem
Stabilization using a direct eigenvalue optimization approach
Output feedback stabilization: the single delay case
Output feedback stabilization: the multiple delay case
Congestion control algorithms in networks
Smith predictor for stable systems: delay sensitivity analysis
Controlling unstable systems using finite spectrum assignment
Consensus problems in traffic flow applications
Stability analysis of delay models in biosciences
Table of Contents provided by Publisher. All Rights Reserved.

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