Skip to main content

Robust Control of Infinite-Dimensional Systems

  • Living reference work entry
  • Latest version View entry history
  • First Online:
Encyclopedia of Systems and Control
  • 74 Accesses

Abstract

Basic robust control problems are studied for the feedback systems where the underlying plant model is infinite dimensional. The \(\mathcal {H}_\infty \) optimal controller formula is given for the mixed sensitivity minimization problem with rational weights. Key steps of the numerical computations required to determine the controller parameters are illustrated with an example where the plant model includes time delay terms.

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

Access this chapter

Institutional subscriptions

Bibliography

  • Curtain R, Morris K (2009) Transfer functions of distributed parameter systems: a tutorial. Automatica 45:1101–1116

    Article  MathSciNet  Google Scholar 

  • Curtain R, Zwart HJ (1995) An introduction to infinite-dimensional linear systems theory. Springer, New York

    Book  Google Scholar 

  • Desoer CA, Vidyasagar M (2009) Feedback systems: input-output properties. SIAM, Philadelphia

    Book  Google Scholar 

  • Doyle JC, Francis BA, Tannenbaum AR (1992) Feedback control theory. Macmillan, New York

    Google Scholar 

  • Foias C, Özbay H, Tannenbaum A (1996) Robust control of infinite-dimensional systems: frequency domain methods. Lecture notes in control and information sciences, vol 209. Springer, London

    MATH  Google Scholar 

  • Gu G, Khargonekar PP, Lee EB (1989) Approximation of infinite-dimensional systems. IEEE Trans Autom Control 34:610–618

    Article  MathSciNet  Google Scholar 

  • Gumussoy S (2011) Coprime-inner/outer factorization of SISO time-delay systems and FIR structure of their optimal \(\mathcal {H}_\infty \) controllers. Int J Robust Nonlinear Control 22:981–998

    Google Scholar 

  • Gumussoy S, Michiels W (2011) Fixed-order H-infinity control for interconnected systems using delay differential algebraic equations. SIAM J Control Optim 49(5):2212–2238

    Article  MathSciNet  Google Scholar 

  • Gumussoy S, Özbay H (2004) On the mixed sensitivity minimization for systems with infinitely many unstable modes. Syst Control Lett 53:211–216

    Article  MathSciNet  Google Scholar 

  • Meinsma G, Mirkin L, Zhong Q-C (2002) Control of systems with I/O delay via reduction to a one-block problem. IEEE Trans Autom Control 47:1890–1895

    Article  MathSciNet  Google Scholar 

  • Monje CA, Chen YQ, Vinagre BM, Xue D, Feliu V (2010) Fractional-order systems and controls, fundamentals and applications. Springer, London

    MATH  Google Scholar 

  • Morris KA (2001) \(\mathcal {H}_\infty \)-output feedback of infinite-dimensional systems via approximation. Syst Control Lett 44:211–217

    Article  MathSciNet  Google Scholar 

  • Özbay H (2000) Introduction to feedback control theory. CRC Press LLC, Boca Raton

    MATH  Google Scholar 

  • Özbay H (2010) Stable \(\mathcal {H}_\infty \) controller design for systems with time delays. In: Willems JC et al (eds) Perspectives in mathematical system theory, control, and signal processing. Lecture notes in control and information sciences, vol 398. Springer, Berlin/Heidelberg, pp 105–113

    Google Scholar 

  • Özbay H, Gumussoy S, Kashima K, Yamamoto Y (2018) Frequency domain techniques for H control of distributed parameter systems. SIAM, Philadelphia

    Book  Google Scholar 

  • Sipahi R, Niculescu S-I, Abdallah CT, 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 

  • Stein G (2003) Respect the unstable. IEEE Control Syst Mag 23(4):12–25

    Article  Google Scholar 

  • van Keulen B (1993) \(\mathcal {H}_\infty \)-control for distributed parameter systems: a state space approach. Birkhäuser, Boston

    Google Scholar 

  • Wakaiki M, Yamamoto Y, Özbay H (2013) Stable controllers for robust stabilization of systems with infinitely many unstable poles. Syst Control Lett 62:511–516

    Article  MathSciNet  Google Scholar 

  • Zhong QC (2006) Robust control of time-delay systems. Springer, London

    MATH  Google Scholar 

  • Zhou K, Doyle JC, Glover K (1996) Robust and optimal control. Prentice-Hall, Upper Saddle River

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Hitay Özbay .

Editor information

Editors and Affiliations

Section Editor information

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer-Verlag London Ltd., part of Springer Nature

About this entry

Check for updates. Verify currency and authenticity via CrossMark

Cite this entry

Özbay, H. (2019). Robust Control of Infinite-Dimensional Systems. In: Baillieul, J., Samad, T. (eds) Encyclopedia of Systems and Control. Springer, London. https://doi.org/10.1007/978-1-4471-5102-9_162-2

Download citation

  • DOI: https://doi.org/10.1007/978-1-4471-5102-9_162-2

  • 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

    Robust Control of Infinite-Dimensional Systems
    Published:
    29 August 2019

    DOI: https://doi.org/10.1007/978-1-4471-5102-9_162-2

  2. Original

    Robust control of infinite dimensional systems
    Published:
    11 February 2014

    DOI: https://doi.org/10.1007/978-1-4471-5102-9_162-1