Skip to main content
SpringerLink
Log in

Dynamic feedback transformations of controllable linear time-varying systems

  • Conference paper
  • First Online:
Nonlinear control in the year 2000 volume 2

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 259))

Abstract

We show that a linear time-varying single-input system of state dimension n which is N-controllable (N ≥ n) can be transformed into a chain of integrators by an exogenous dynamic feedback of size N — n and a change of coordinates.

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

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. P. Brunovský. A classification of linear controllable systems. Kybernetika, 6(3):173–188, 1970.

    MathSciNet  Google Scholar 

  2. M. Fliess, J. Lévine, Ph. Martin, and P. Rouchon. A Lie-Bäcklund approach to equivalence and flatness of nonlinear systems. IEEE Trans. Automat. Control, 44:922–937, 1999.

    Article  MATH  MathSciNet  Google Scholar 

  3. B. Jakubczyk and W. Respondek. On linearization of control systems. Bull. Acad. Pol. Sci. Ser. Sci. Math., 28:517–522, 1980.

    MATH  MathSciNet  Google Scholar 

  4. T. Kailath. Linear Systems. Prentice-Hall, 1980.

    Google Scholar 

  5. E. W. Kamen, P. P. Khargonekar, and K. R. Poolla. A transfer-function approach to linear time-varying discrete-time systems. SIAM J. Control & Opt., 23(4):550–565, 1985.

    Article  MATH  MathSciNet  Google Scholar 

  6. B. Malgrange. Lettre du 26 janvier. Communication personnelle.

    Google Scholar 

  7. Ph. Martin, R. Murray, and P. Rouchon. Flat systems. In Proc. of the 4th European Control Conf., pages 211–264, Brussels, 1997. Plenary lectures and Mini-courses.

    Google Scholar 

  8. A. S. Morse and L. M. Silverman. Structure of index-invariant systems. SIAM J. Control, 11(2):215–225, 1973.

    Article  MATH  MathSciNet  Google Scholar 

  9. L. M. Silverman and H. E. Meadows. Controllability and observability in time-variable linear systems. SIAM J. Control, 5:64–73, 1967.

    Article  MATH  MathSciNet  Google Scholar 

  10. E. D. Sontag. Controllability and linearized regulation. IEEE Trans. Automat. Control, AC-32(10):877–888, 1987.

    Article  MathSciNet  Google Scholar 

  11. E. D. Sontag. Mathematical Control Theory. Springer, 2nd edition, 1991.

    Google Scholar 

  12. W. A. Wolovich. On the stabilization of controllable systems. IEEE Trans. Automat. Control, AC-13:569–572, 1968.

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Centre Automatique et Systèmes, École des Mines de Paris, 35 rue Saint-Honoré, 77305, Fontainebleau Cedex, France

    François Malrait, Philippe Martin & Pierre Rouchon

Authors
  1. François Malrait
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Philippe Martin
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Pierre Rouchon
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Alberto Isidori Françoise Lamnabhi-Lagarrigue Witold Respondek

Rights and permissions

Reprints and permissions

Copyright information

© 2001 Springer-Verlag London Limited

About this paper

Cite this paper

Malrait, F., Martin, P., Rouchon, P. (2001). Dynamic feedback transformations of controllable linear time-varying systems. In: Isidori, A., Lamnabhi-Lagarrigue, F., Respondek, W. (eds) Nonlinear control in the year 2000 volume 2. Lecture Notes in Control and Information Sciences, vol 259. Springer, London. https://doi.org/10.1007/BFb0110291

Download citation

  • DOI: https://doi.org/10.1007/BFb0110291

  • Published:

  • Publisher Name: Springer, London

  • Print ISBN: 978-1-85233-364-5

  • Online ISBN: 978-1-84628-569-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation