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Stability and Stabilization of Time-Delay Systems

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

Part of Advances in Design and Control

  • Date Published: February 2008
  • availability: This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial & Applied Mathematics for availability.
  • format: Paperback
  • isbn: 9780898716320


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About the Authors
  • 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.

    • Presents a unifying, eigenvalue based approach
    • Demonstrates a large potential for handling biological models, networks and engineering applications
    • Uses a cross-fertilisation of results from control theory, numerical linear algebra, numerical bifurcation analysis and optimisation
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    Product details

    • Date Published: February 2008
    • format: Paperback
    • isbn: 9780898716320
    • length: 400 pages
    • dimensions: 254 x 178 x 20 mm
    • weight: 0.67kg
    • availability: This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial & Applied Mathematics for availability.
  • Table of Contents

    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

  • Authors

    Wim Michiels, Katholieke Universiteit Leuven, Belgium
    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, Centre National de la Recherche Scientifique (CNRS), Paris
    Silviu-Iulian Niculescu is the Research Director at CNRS L2S (Laboratory of Signals and Systems), Gif-sur-Yvette, France.

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