Skip to main content
Log in

Zeros at infinity for nonlinear discrete time systems

  • Published:
Mathematical systems theory Aims and scope Submit manuscript

Abstract

A new set of integer invariants of a discrete time nonlinear system is introduced. Following the linear and continuous time nonlinear theory, this set is called the structure at infinity of the system. These integers contain structural information about the system. To support this idea the general block decoupling problem and a special case of the noninteracting control problem are solved in terms of the zeros at infinity.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. M. Fliess, Fonctioneless causales non linéares et interdéterminées non commutative,Bull. Soc. Math., France 109, 3–40 (1981).

    Google Scholar 

  2. J. W. Grizzle, Controlled invariance for discrete time nonlinear systems with an application to the disturbance decoupling problem, to appear inIEEE-T-AC (1985).

  3. J. W. Grizzle, Local input-output decoupling of discrete time nonlinear systems, to appear inInt. J. of Control.

  4. A. Isidori, A. J. Krener, C. Gori-Giorgi, S. Monaco, Nonlinear decoupling via feedback: A differential geometric approach,IEEE-T-AC 26, 331–345 (1981).

    Google Scholar 

  5. A. Isidori, Control of nonlinear systems via dynamic state-feedback, in the proceedings of theConference sur les méthodes algèbriques et gémétriques en automatique non linéaire, Paris, France, June 3–7, 1985.

  6. T. Kailath,Linear Systems, Prentice-Hall, Englewood Cliffs, 1980.

    Google Scholar 

  7. M. Malabre, Structure à l'infini des triplets invariants. Applications à la poursuite parfait de modèle, inAnalysis and Optimization of Systems (Eds. A. Bensoussan and J. L. Lions),Lecture Notes in Control and Information Sciences 44, 43–53, 1982.

    Google Scholar 

  8. A. Monaco and D. Normand-Cycrot, The immersion under feedback of a multidimensional discrete time nonlinear system in to a linear system,Int. J. Contr., 38, 245–161, 1983.

    Google Scholar 

  9. A. Monaco and D. Normand-Cycrot, Some remarks on the invertibility of nonlinear discrete time systems, American Control Conference, San Francisco, 1983.

    Google Scholar 

  10. A. Monaco and D. Normand-Cycrot, Sur la commande non interactive de systèmes non linéaires en temps discret,In Analysis and Optimization of Systems (Eds. A. Bensoussan and J. L. Lions),Lecture Notes in Control and Information Sciences 63, 364–377, 1984.

    Google Scholar 

  11. A. Monaco and D. Normand-Cycrot, Sur la subordination d'un système non linéaire à un système linéaire, Actes du Colleque National CNRS-RCP 567:Développement et utilisation d'outils et modèles mathematiques en automatique, analyse des systèmes et traitement du signel (Ed. I. D. Landau) Eds. du CNRS Paris 3, 1983.

  12. P. B. C. Moore and A. J. Laub, Computation of supremal (A, B)-invariant and (A, B)-controllability subspaces”,IEEE-T-AC, 23, 783–792, (1978).

    Google Scholar 

  13. H. Nijmeijer, Zeros at infinity for nonlinear systems, what are they and what are they good for?, to appear inProceedings of Int. School on Geometric Methods in Nonlinear Systems Theory, Bierutowice, Poland 1984.

    Google Scholar 

  14. H. Nijmeijer, Right-invertibility for nonlinear control systems: a geometric approach, preprint 1984, revised version 1985.

  15. H. Nijmeijer and J. M. Schumacher, Zeros at infinity for affine nonlinear control systems,IEEE-T-AC 30, 566–573, 1985.

    Google Scholar 

  16. W. Respondek, On decomposition of nonlinear control systems,Syst. Conr. Lett. 1, 301–308, 1982.

    Google Scholar 

  17. W. M. Wonham,Linear Multivariable Control: A Geometric Approach, 2nd ed. Springer, Berlin, 1979.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Partially supported by NSF contract ECS-8505318.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Grizzle, J.W., Nijmeijer, H. Zeros at infinity for nonlinear discrete time systems. Math. Systems Theory 19, 79–93 (1986). https://doi.org/10.1007/BF01704907

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01704907

Keywords

Navigation