Encyclopedia of Systems and Control

Living Edition
| Editors: John Baillieul, Tariq Samad

Control of Linear Systems with Delays

  • Wim MichielsEmail author
Living reference work entry

Latest version View entry history

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

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.

Keywords

Delay differential equations; Delays as controller parameters; Functional differential equation 
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Notes

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.

Bibliography

  1. Bellen E, Zennaro M (2013) Numerical methods for delay differential equations. Oxford University Press, OxfordzbMATHGoogle Scholar
  2. Fridman E (2014) Introduction to time-delay systems. Analysis and control. Birkhäuser, BaselCrossRefGoogle Scholar
  3. Gu K, Kharitonov VL, Chen J (2003) Stability of time-delay systems. Birkhäuser, BaselCrossRefGoogle Scholar
  4. Kharitonov VL (2013) Time-delay systems. Lyapunov functionals and matrices. Birkhäuser, BaselCrossRefGoogle Scholar
  5. Krstic M (2009) Delay compensation for nonlinear, adaptive, and PDE systems. Birkhäuser, BaselCrossRefGoogle Scholar
  6. 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 201–216CrossRefGoogle Scholar
  7. Michiels W, Niculescu S-I (2014) Stability, control, and computation for time-delay systems. An eigenvalue based approach, 2nd edn. SIAM, PhiladelphiaGoogle Scholar
  8. Niculescu S-I (2001) Delay effects on stability: a robust control approach. Lecture notes in control and information sciences, vol 269. Springer, Berlin/New YorkzbMATHGoogle Scholar
  9. Richard J-P (2003) Time-delay systems: an overview of recent advances and open problems. Automatica 39(10):1667–1694MathSciNetCrossRefGoogle Scholar
  10. 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):38–65MathSciNetCrossRefGoogle Scholar

Copyright information

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

Authors and Affiliations

  1. 1.Numerical Analysis and Applied Mathematics SectionKU LeuvenLeuven (Heverlee)Belgium

Section editors and affiliations

  • Miroslav Krstic
    • 1
  1. 1.Department of Mechanical and Aerospace EngineeringUniversity of CaliforniaSan Diego, La JollaUSA