Skip to main content
SpringerLink
Log in

Matrix inequality conditions for canonical factorization of rational transfer function matrices

  • Chapter
Open Problems in Mathematical Systems and Control Theory

Part of the book series: Communications and Control Engineering ((CCE))

  • 919 Accesses

Abstract

A canonical factorization of a square real-rational transfer function matrix M(s) is the following:

$$ M\left( s \right) = {M_ + }\left( s \right)M\_\left( s \right), $$

where M + (s), M + (s) −1, M_(−s), and M_(−s) −1 belong to RH∞.

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

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Similar content being viewed by others

References

  1. D. C. Youla, “On the factorization of rational matrices,” IRE Trans. Information Theory, vol. IT-7, pp. 172–189 (1961).

    Google Scholar 

  2. B. Anderson and S. Vongpanitlerd, Network analysis and synthesis: a modern systems theory approach. Prentice-Hall, 1973.

    Google Scholar 

  3. J. C. Willems, “Least squares stationary optimal control and the algebraic Riccati equation,” IEEE Trans. Aut. Control, vol. AC-16, pp. 621–634 (1971).

    Article  MathSciNet  Google Scholar 

  4. A. Rantzer, “A note on the Kaiman-Yacubovich-Popovlemma,” in Proceedings of 3rd European Control Conference, pp. 1792–1795, 1995.

    Google Scholar 

  5. C. A. Desoer and M. Vidyasagar, Feedback Systems: Input-Output Properties. New York: Academic Press, 1975.

    MATH  Google Scholar 

  6. V. Balakrishnan, “Linear matrix inequalities in robustness analysis with multipliers,” Syst. Control Letters, vol. 25, no. 4, pp. 265–272 (1995).

    Article  MATH  Google Scholar 

  7. B. A. Francis, A course in H∞ Control Theory, vol. 88 of Lecture Notes in Control and Information Sciences. Springer-Verlag, 1987.

    Google Scholar 

  8. H. Bart, I. Gohberg, and M. A. Kaashoek, Minimal Factorization of Matrix and Operator Functions. Basel: Birkhauser, 1979.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Electrical and Computer Engineering, Purdue University, West Lafayette, IN, 47907-1285, USA

    Venkataramanan Balakrishnan

Authors
  1. Venkataramanan Balakrishnan
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Institute of Mathematics, University of Leige, Sart Tilman B37, B-4000, Liege, Belgium

    Vincent Blondel (PhD) (PhD)

  2. Department of Mathematics, Rutgers University, Hill Center 724, 08903, New Brunswick, USA

    Eduardo D. Sontag (PhD) (PhD)

  3. Centre for Arificial Intelligence and Robotics, Raj Bhavan Cirlce - High Grounds, 560001, Bangalore, India

    Mathukumalli Vidyasagar (PhD) (PhD)

  4. Institute of Mathematics, Rijksuniversiteit te Groningen, Postbus 800, 9700, Av Groningen, The Netherlands

    Jan C. Willems (PhD) (PhD)

Rights and permissions

Reprints and permissions

Copyright information

© 1999 Springer-Verlag London Limited

About this chapter

Cite this chapter

Balakrishnan, V. (1999). Matrix inequality conditions for canonical factorization of rational transfer function matrices. In: Blondel, V., Sontag, E.D., Vidyasagar, M., Willems, J.C. (eds) Open Problems in Mathematical Systems and Control Theory. Communications and Control Engineering. Springer, London. https://doi.org/10.1007/978-1-4471-0807-8_7

Download citation

  • DOI: https://doi.org/10.1007/978-1-4471-0807-8_7

  • Publisher Name: Springer, London

  • Print ISBN: 978-1-4471-1207-5

  • Online ISBN: 978-1-4471-0807-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation