Skip to main content
SpringerLink
Log in

Eigenvalue localization ofG-stable matrix polytopes

  • Communication Briefs
  • Published:
Multidimensional Systems and Signal Processing Aims and scope Submit manuscript

Abstract

A simple geometric test can be applied to evaluateG-stability of a polytope of matrices. In case of a regionG being a convex subset of the complex plane, it suffices to assume that four (for some regions even less) corner points of a certain rectangle are contained inG.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  1. R. Rockefellar,Convex analysis, Princeton, NJ, Princeton University Press, 1970.

    Google Scholar 

  2. A.C. Bartlett, C.V. Hollot et al., “Root Location of an Entire Polytope: It suffices to Check the Edges,”Mathematics of Control, Signals and Systems, vol. 1, 1988, pp. 61–71.

    Google Scholar 

  3. B.R. Barmish, M. Fu et al., “Stability of a Polytope of Matrices: Counterexamples,”IEEE Transactions on Automatic Control, vol. AC-33, no. 6, 1988, pp. 569–572.

    Google Scholar 

  4. Y.C. Soh and Y.K. Foo, “Comments on ‘Stability of Polytope of Matrices: Counterexamples’,”IEEE Transactions on Automatic Control, vol. 34, no. 12, 1989.

  5. Y.K. Foo and Y.C. Soh, “Stability Analysis of a Family of Matrices,”IEEE Transactions on Automatic Control, vol. AC-35, no. 11, 1990.

  6. F.R. Gantmacher,The Theory of Matrices, vol. 1, New York: Chelsea, 1977.

    Google Scholar 

  7. R. Bellman,Introduction to Matrix Analysis, New York, McGraw-Hill, 1960.

    Google Scholar 

  8. J.N. Franklin,Matrix Theory, Englewood Cliffs, NJ: Prentice-Hall, 1968.

    Google Scholar 

  9. R.W. Brockett,Finite Dimensional Linear Systems, New York, Wiley, 1970.

    Google Scholar 

  10. M. Marcus and H. Minc,A Survey of Matrix Theory and Matrix Inequalities, Boston: Allyn & Bacon, 1964.

    Google Scholar 

  11. S. Barnett and R.E. Scranton, “Location of Matrix Eigenvalues in the Complex Plane,”IEEE Transactions on Automatic Control, vol. AC-27, no. 4, 1982.

  12. Y.-T. Juang, “Reduced Conservatism of Eigenvalue Estimation,”IEEE Transactions on Automatic Control, vol. 34, no. 9, 1989.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Fundamental Research, Institute of Electrical Engineering, ul. Pozaryskiego 28, 04-704, Warsaw, Poland

    Marek K. Solak

  2. Department of Industrial and Engineering Technology, Central Michigan University, 48859, Mount Pleasant, MI

    Albert C. Peng

Authors
  1. Marek K. Solak
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Albert C. Peng
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Solak, M.K., Peng, A.C. Eigenvalue localization ofG-stable matrix polytopes. Multidim Syst Sign Process 5, 307–318 (1994). https://doi.org/10.1007/BF00980713

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00980713

Key Words

Search

Navigation