Skip to main content
SpringerLink
Log in
Book cover

Encyclopedia of Systems and Control pp 1–7Cite as

Control of Linear Systems with Delays

Abstract

The presence of time delays in dynamical systems may induce complex behavior, and this behavior is not always intuitive. Even if a system’s equation is scalar, oscillations may occur. Time delays in control loops are usually associated with degradation of performance and robustness, but, at the same time, there are situations where time delays are used as controller parameters.

This is a preview of subscription content, log in via an institution.

Bibliography

  • Bellen E, Zennaro M (2013) Numerical methods for delay differential equations. Oxford University Press, Oxford

    MATH  Google Scholar 

  • Fridman E (2014) Introduction to time-delay systems. Analysis and control. Birkhäuser, Basel

    Book  Google Scholar 

  • Gu K, Kharitonov VL, Chen J (2003) Stability of time-delay systems. Birkhäuser, Basel

    Book  Google Scholar 

  • Kharitonov VL (2013) Time-delay systems. Lyapunov functionals and matrices. Birkhäuser, Basel

    Book  Google Scholar 

  • Krstic M (2009) Delay compensation for nonlinear, adaptive, and PDE systems. Birkhäuser, Basel

    Book  Google Scholar 

  • Michiels W (2012) Design of fixed-order stabilizing and \({\mathcal {H}}_2 -{\mathcal {H}}_\infty \) optimal controllers: an eigenvalue optimization approach. In: Time-delay systems: methods, applications and new trends. Lecture notes in control and information sciences, vol 423. Springer, Berlin/Heidelberg, pp 201–216

    Chapter  Google Scholar 

  • Michiels W, Niculescu S-I (2014) Stability, control, and computation for time-delay systems. An eigenvalue based approach, 2nd edn. SIAM, Philadelphia

    Google Scholar 

  • Niculescu S-I (2001) Delay effects on stability: a robust control approach. Lecture notes in control and information sciences, vol 269. Springer, Berlin/New York

    MATH  Google Scholar 

  • Richard J-P (2003) Time-delay systems: an overview of recent advances and open problems. Automatica 39(10):1667–1694

    Article  MathSciNet  Google Scholar 

  • Sipahi R, Niculescu S, Abdallah C, Michiels W, Gu K (2011) Stability and stabilization of systems with time-delay. IEEE Control Syst Mag 31(1):38–65

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

The author received funding from the project C14/17/072 of the KU Leuven Research Council, the project G0A5317N of the Research Foundation-Flanders (FWO - Vlaanderen), and from the project UCoCoS, funded by the European Unions Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie Grant Agreement No 675080.

Author information

Authors and Affiliations

  1. Numerical Analysis and Applied Mathematics Section, KU Leuven, Leuven (Heverlee), Belgium

    Wim Michiels

Authors
  1. Wim Michiels
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Wim Michiels .

Editor information

Editors and Affiliations

  1. Electrical and Computer Engineering, Boston University, Boston, MA, USA

    John Baillieul

  2. Automation and Control Solutions, Honeywell, Golden Valley, MN, USA

    Tariq Samad

Section Editor information

  1. Department of Mechanical and Aerospace Engineering, University of California, San Diego, La Jolla, CA, USA

    Miroslav Krstic

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer-Verlag London Ltd., part of Springer Nature

About this entry

Check for updates. Verify currency and authenticity via CrossMark

Cite this entry

Michiels, W. (2020). Control of Linear Systems with Delays. In: Baillieul, J., Samad, T. (eds) Encyclopedia of Systems and Control. Springer, London. https://doi.org/10.1007/978-1-4471-5102-9_16-3

Download citation

  • DOI: https://doi.org/10.1007/978-1-4471-5102-9_16-3

  • Published:

  • Publisher Name: Springer, London

  • Print ISBN: 978-1-4471-5102-9

  • Online ISBN: 978-1-4471-5102-9

  • eBook Packages: Springer Reference EngineeringReference Module Computer Science and Engineering

Publish with us

Policies and ethics

Chapter history

  1. Latest

    Control of Linear Systems with Delays
    Published:
    27 December 2019

    DOI: https://doi.org/10.1007/978-1-4471-5102-9_16-4

  2. Control of Linear Systems with Delays
    Published:
    08 November 2019

    DOI: https://doi.org/10.1007/978-1-4471-5102-9_16-3

  3. Control of Linear Systems with Delays
    Published:
    28 November 2014

    DOI: https://doi.org/10.1007/978-1-4471-5102-9_16-2

  4. Original

    Control of Linear Systems with Delays
    Published:
    12 March 2014

    DOI: https://doi.org/10.1007/978-1-4471-5102-9_16-1

Search

Navigation