Skip to main content
SpringerLink
Log in

On the Local Sensitivity of the Discrete-Time \(\cal H_{\infty}\) Control Problem

  • Conference paper
Numerical Analysis and Its Applications (NAA 2008)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5434))

Included in the following conference series:

  • 1765 Accesses

Abstract

In this paper linear perturbation bounds are obtained for the linear matrix inequalities (LMI) arising in the discrete-time \(\cal H_{\infty}\) control problem. The sensitivity analysis of the perturbed LMI is carried out in a similar way as for perturbed matrix equations, after introducing a suitable right hand side which is slightly perturbed.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Boyd, S., El Ghaoui, L., Feron, E.: Linear matrix inequalities in systems and control theory. SIAM Philladelphia 41(3), 358–367 (1996)

    Google Scholar 

  2. Doyle, J.C., Glover, K., Khargonekar, P.P., Francis, B.A.: State-Space Solutions to Standard H 2 and H  ∞  Control Problems. IEEE Transactions on Automatic Control 34, 831–847 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  3. Gahinet, P., Apkarian, P.: A linear matrix inequality approach to H  ∞  control. Int. J. Robust Non. Contr. 4, 421–448 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  4. Gahinet, P., Nemirovski, A., Laub, A., Chilali, M.: LMI Control Toolbox for Use with MATLAB. The MathWorks, Inc (2000)

    Google Scholar 

  5. Nesterov, Y., Nemirovski, A.: Interior–Point Polynomial Algorithms in Convex Programming. SIAM, Philadephia (1994)

    Book  Google Scholar 

  6. Peterson, I.R., Anderson, B.D.O., Jonkheere, E.A.: A first principles solution to the non-singular H  ∞  control problem. Int. J. Robust Non. Contr. 1, 171–185 (1991)

    Article  Google Scholar 

  7. Steward, G., Sun, J.G.: Matrix Perturbation Theory. Academic Press, N.Y (1990)

    Google Scholar 

  8. Zhou, K., Doyle, J.C., Glover, K.: Robust and Optimal Control. Prentice-Hall, Upper Saddle River (1995)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Technical University of Sofia, 1000, Sofia, Bulgaria

    A. S. Yonchev & P. Hr. Petkov

  2. Université des Sciences et Technologies de Lille, 59655, Villeneuve d’Ascq, France

    N. D. Christov

  3. Civil Engineering and Geodesy, University of Architecture, 1046, Sofia, Bulgaria

    M. M. Konstantinov

Authors
  1. A. S. Yonchev
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. P. Hr. Petkov
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. N. D. Christov
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. M. M. Konstantinov
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Institute for Parallel Processing, Bulgarian Academy of Sciences, Acad. G. Bonchev Str. Bl. 25-A, 1113, Sofia, Bulgaria

    Svetozar Margenov

  2. FNSE, Department of Numerical Methods and Statistics, University of Rousse, 8 Studentska str., 7017, Rousse, Bulgaria

    Lubin G. Vulkov

  3. Department of Informatics and Mathematical Modelling, Technical University of Denmark, 2800, Kongens, Lyngby, Denmark

    Jerzy Waśniewski

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Yonchev, A.S., Petkov, P.H., Christov, N.D., Konstantinov, M.M. (2009). On the Local Sensitivity of the Discrete-Time \(\cal H_{\infty}\) Control Problem. In: Margenov, S., Vulkov, L.G., Waśniewski, J. (eds) Numerical Analysis and Its Applications. NAA 2008. Lecture Notes in Computer Science, vol 5434. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00464-3_71

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-00464-3_71

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-00463-6

  • Online ISBN: 978-3-642-00464-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation