Skip to main content
SpringerLink
Log in

An elementary proof of the Routh-Hurwitz stability criterion

  • Published:
Circuits, Systems and Signal Processing Aims and scope Submit manuscript

Abstract

This paper presents an elementary proof of the well-known Routh-Hurwitz stability criterion. The novelty of the proof is that it requires only elementary geometric considerations in the complex plane. This feature makes it useful for use in undergraduate control system courses.

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

Similar content being viewed by others

References

  1. Dorf, R. C.,Modern Control Systems, 3rd edn., Addison-Wesley, Reading, MA, 1980.

    Google Scholar 

  2. Gantmacher, F. R.,The Theory of Matrices, Vol. 2, Chelsea, New York, 1959.

    Google Scholar 

  3. Hermite, C., Sur le nombre des racines d'une équation algébrique comprise entre des limites données,J. Reine Angew. Math.,51, 39–51, 1856.

    Google Scholar 

  4. Hurwitz, A., On the conditions under which an equation has only roots with negative real parts,Math. Ann.,46, 273–284, 1895. Also inSelected Papers on Mathematical Trends in Control Theory, Dover, New York, 1964, pp. 70–82.

    Google Scholar 

  5. Kuo, B. C.,Automatic Control Systems, 4th edn., Prentice-Hall Englewood Cliffs, NJ, 1982.

    Google Scholar 

  6. Mansour, M., A Simple Proof of the Routh-Hurwitz Criterion, Report #88-04, Institute of Automatic Control & Industrial Electronics, Swiss Federal Institute of Technology, December, 1988.

  7. Routh, E. J.,A Treatise on the Stability of a Given State of Motion, London, Macmillan, 1877.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Electronics Research Laboratory, Department of Electrical Engineering and Computer Science, University of California, 94720, Berkeley, California, USA

    J. J. Anagnost & C. A. Desoer

Authors
  1. J. J. Anagnost
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. C. A. Desoer
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Research supported by Hughes Aircraft Company, El Segundo, California 90245, USA, and the National Science Foundation under Grant ECS 21818.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Anagnost, J.J., Desoer, C.A. An elementary proof of the Routh-Hurwitz stability criterion. Circuits Systems and Signal Process 10, 101–114 (1991). https://doi.org/10.1007/BF01183243

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01183243

Keywords

Search

Navigation