Skip to main content
SpringerLink
Log in

Examples of stabilization with hybrid feedback

  • Conference paper
  • First Online:
Hybrid Systems III (HS 1995)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1066))

Included in the following conference series:

Abstract

Via examples, this paper examines the possibility of stabilizing a continuous control plant, through an interaction with a discrete time controller. Such a hybrid feedback complements the output feedback within the plant when the latter fails to stabilize the system or fails to produce smooth stabilization. The displayed examples point to both the mathematical and the design challenges that the method poses.

Incumbent of the Hettie H. Heineman Professorial Chair in Mathematics

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. Alur, R., Courcoubetis, C., Henzinger, T.A., Ho, P.-H.: Hybrid automata: an algorithmic approach to the specification and verification of hybrid systems. In: Hybrid Systems, Grossman, R.L. et al. (eds.) (Lecture Notes in Computer Science, vol. 736) Springer-Verlag, Berlin, 1993, pp. 209–229.

    Google Scholar 

  2. Antsaklis, R.J., Stiver, J.A., Lemmon, M.: Hybrid system modeling and autonomous control systems. In: Hybrid Systems, Grossman, R.L. et al. (eds.) (Lecture Notes in Computer Science, vol. 736) Springer-Verlag, Berlin, 1993, pp. 366–392.

    Google Scholar 

  3. Bacciotti, A.: Local Stabilizability of Nonlinear Control Systems. World Scientific, Singapore, 1992.

    Google Scholar 

  4. Branicky, M.S.: Studies in Hybrid Systems: Modelling, Analysis, and Control. Ph.D. Thesis, Massachusetts Institute of Technology, Cambridge, Massachusetts, June 1995.

    Google Scholar 

  5. Guckenheimer, J.: A robust hybrid stabilization strategy for equilibria. IEEE Trans. on Automatic Control 40 (1995) 321–326.

    Article  Google Scholar 

  6. Henzinger, T.H., Ho, P.-H.: Algorithmic analysis of nonlinear hybrid systems. In: Computer Aided Verification, Wolper, P. (ed.) (Lecture Notes in Computer Science, vol. 939) Springer-Verlag, Berlin, 1995, pp. 225–238.

    Google Scholar 

  7. Kompass, E.J.: Open the loop for stable controls. Control Engineering 42, Jan. 1995, p. 126.

    Google Scholar 

  8. LaSalle, J.P.: Asymptotic stability criteria. In: Proc. Symp. Appl. Math. Hydrodynamic Instability, vol. 13, Amer. Math. Soc., Providence, 1962, pp. 299–307.

    Google Scholar 

  9. Nerode, A., Kohn, W.: Models for hybrid systems: Automata, topologies, controllability, observability. In: Hybrid Systems, Grossman, R.L. et al. (eds.) (Lecture Notes in Computer Science, vol. 736) Springer-Verlag, Berlin, 1993, pp. 317–356.

    Google Scholar 

  10. Rouche, N., Habets, P., Laloy, M.: Stability Theory by Liapunov's Direct Method. Springer-Verlag, Berlin, 1977.

    Google Scholar 

  11. Sontag, E.: Nonlinear regulation: The piecewise linear approach. IEEE Trans. on Automatic Control 26 (1981) 346–358.

    Article  Google Scholar 

  12. Sontag, E.: Mathematical Control Theory, Springer-Verlag, New York, 1989.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Theoretical Mathematics, The Weizmann Institute of Science, 76100, Rehovot, Israel

    Zvi Artstein

Authors
  1. Zvi Artstein
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Rajeev Alur Thomas A. Henzinger Eduardo D. Sontag

Rights and permissions

Reprints and permissions

Copyright information

© 1996 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Artstein, Z. (1996). Examples of stabilization with hybrid feedback. In: Alur, R., Henzinger, T.A., Sontag, E.D. (eds) Hybrid Systems III. HS 1995. Lecture Notes in Computer Science, vol 1066. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0020944

Download citation

  • DOI: https://doi.org/10.1007/BFb0020944

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-61155-4

  • Online ISBN: 978-3-540-68334-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation