Skip to main content
SpringerLink
Log in

On the stabilizability of homogeneous control systems

  • Nonlinear Systems
  • Conference paper
  • First Online:
Book cover Analysis and Optimization of Systems

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 111))

  • 2025 Accesses

Abstract

This note is concerned with linear and/or homogeneous stabilization of systems with nonlinear but homogeneous drift term. Local and global features of the closed-loop system are discussed. Our results apply also in the case of higher order perturbations.

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. A. Andreini, A. Bacciotti and G. Stefani, Global Stabilizability of Homogeneous Vector Fields of Odd Degree, to appear in Systems and Control Letters

    Google Scholar 

  2. V. Arnold, Chapitres supplémentaires de la théorie des équations différentielles ordinaires, MIR Moscou, 1980

    Google Scholar 

  3. A. Bacciotti, Further Remarks on Potentially Global Stabilizability, Submitted

    Google Scholar 

  4. J. Baillieul, The Geometry of Homogeneous Polynomial Dynamical Systems, Nonlinear Analysis TMA, 4 (1980), pp. 879–900

    Google Scholar 

  5. B. Bonnard, Esquisse d'une théorie des systèmes quadratique, Thèse d'Etat, Grenoble, Juin 1983

    Google Scholar 

  6. J. Carr, Applications of Center Manifold Theory, Springer Verlag, New York, 1981

    Google Scholar 

  7. W. Hahn, Stability of Motion, Springer Verlag, Berlin, 1967

    Google Scholar 

  8. V. Jurdjevic and I. Kupka, Polynomial Control Systems, Math. Ann., 272 (1985) pp. 361–368

    Google Scholar 

  9. D.E. Koditschek and K.S. Narendra, Stability of Second Order Quadratic Differential Equations, IEEE Trans. AC-27, (1982) pp. 783–798.

    Google Scholar 

  10. H. Kunita, On the Controllability of Nonlinear Systems with Applications to Polynomial Systems, Appl. Math. Optim., 5 (1979), pp. 89–99.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Istituto di Matematica Applicata, Via S. Marta 3, 50139, Firenze, Italy

    Alessandra Andreini

  2. Dipartimento di Matematica del Politecnico, Corso Duca degli Abruzzi 24, 10129, Torino, Italy

    Andrea Bacciotti

  3. Dipartimento di Matematica e Applicazioni, Via Mezzocannone 8, 80134, Napoli, Italy

    Gianna Stefani

Authors
  1. Alessandra Andreini
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Andrea Bacciotti
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Gianna Stefani
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

A. Bensoussan J. L. Lions

Rights and permissions

Reprints and permissions

Copyright information

© 1988 Springer-Verlag

About this paper

Cite this paper

Andreini, A., Bacciotti, A., Stefani, G. (1988). On the stabilizability of homogeneous control systems. In: Bensoussan, A., Lions, J.L. (eds) Analysis and Optimization of Systems. Lecture Notes in Control and Information Sciences, vol 111. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0042218

Download citation

  • DOI: https://doi.org/10.1007/BFb0042218

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-19237-4

  • Online ISBN: 978-3-540-39161-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation