Skip to main content
SpringerLink
Log in

Nonlinear decoupling and structure at infinity

  • Published:
Mathematics of Control, Signals and Systems Aims and scope Submit manuscript

Abstract

In this paper we characterize the solvability of nonlinear decoupling problems (static or dynamic) through the notion of structure at infinity. This structure is specified by a list of easily computed integers, which are related to the differential output rank. Our notion of structure at infinity generalizes concepts previously introduced for restricted classes of systems such as those linearizable under feedback.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. M. D. di Benedetto, On the equivalence of the invariant subdistribution algorithm and the structure algorithm,Systems Control Lett.,8 (1986), 137–145.

    Article  MathSciNet  Google Scholar 

  2. C. Commault and J. M. Dion, Structure at infinity of linear multivariable systems: a geometric approach,IEEE Trans. Automat. Control,27 (1982), 693–696.

    Article  MathSciNet  Google Scholar 

  3. C. Commault, J. Descusse, J. M. Dion, J. F. Lafay, and M. Malabre, About new decoupling invariants: the essential orders,Internat. J. Control,44 (1986), 689–700.

    Google Scholar 

  4. G. Conte, C. H. Moog, and A. M. Perdon, Un Théorème sur la Représentation Entrée-Sortie d’un Système Non Linéaire, preprint, 1987.

  5. J. Descusse and J. M. Dion, On the structure at infinity of linear square decoupled systems,IEEE Trans. Automat. Control,27 (1982), 971–974.

    Article  MathSciNet  Google Scholar 

  6. J. Descusse and C. H. Moog, Decoupling with dynamic compensation for strong invertible affine nonlinear systems,Internat. J. Control,42 (1985), 1387–1398.

    MathSciNet  Google Scholar 

  7. J. Descusse and C. H. Moog, Dynamic decoupling for right-invertible nonlinear systems,Systems Control Lett.,8 (1987), 345–349.

    Article  MathSciNet  Google Scholar 

  8. M. Fliess, A new approach to the noninteracting control problem in nonlinear systems theory,Proceedings of the 23rd Allerton Conference, Monticello, IL, 1985, pp. 123–129.

  9. M. Fliess, A new approach to the structure at infinity of nonlinear systems,Systems Control Lett.,7 (1986), 419–421.

    Article  MathSciNet  Google Scholar 

  10. M. Fliess, A note on the invertibility of nonlinear input-output differential systems,Systems Control Lett.,8 (1986), 147–151.

    Article  MathSciNet  Google Scholar 

  11. R. M. Hirschorn, Invertibility of multivariable nonlinear control systems,IEEE Trans. Automat. Control,24 (1979), 855–865.

    Article  MathSciNet  Google Scholar 

  12. A. Isidori, Nonlinear feedback, structure at infinity and the input-output linearization problem, inProceedings of MTNS 83, Beer Sheva (P. A. Fuhrmann, ed.), pp. 473–493, Lecture Notes in Control and Information Sciences, Vol. 58, Springer-Verlag, Berlin, 1984.

    Google Scholar 

  13. A. Isidori, Control of nonlinear systems via dynamic state-feedback, inAlgebraic and Geometric Methods in Nonlinear Control Theory (Proc. Conf., Paris, 1985) (M. Fliess and M. Hazewinkel, eds.), pp. 121–145, Reidel, Dordrecht, 1986.

    Google Scholar 

  14. A. Isidori and C. H. Moog, On the nonlinear equivalent of the notion of transmission zeros, inModelling and Adaptive Control (Proc. I.I.A.S.A. Conf., Sopron, 1986) (C. I. Byrnes and A. Kurszanski, eds.), Lecture Notes in Control and Information Sciences, Springer-Verlag, Berlin (to appear).

  15. A. Isidori, C. H. Moog, and A. de Luca, A sufficient condition for full linearization via dynamic state-feedback,Proceedings of the 25th CDC, Athens 1986, pp. 203–208.

  16. M. Malabre,Structure à l’Infini des Triplets Invariants—Application à la Poursuite Parfaite de Modèle pp. 43–53, Lecture Notes in Control and Information Sciences, Vol. 44, Springer-Verlag, Berlin, 1982.

    Google Scholar 

  17. M. Malabre, A complement about the structure of linear systems,Systems Control Lett.,4 (1984), 339–342.

    Article  MathSciNet  Google Scholar 

  18. C. H. Moog, Inversion, Découplage et Poursuite de Modèle des Systèmes Non Linéaires, Thèse d’Etat, University of Nantes, 1987.

  19. H. Nijmeijer and W. Respondek, Decoupling via dynamic compensation for nonlinear control systems,Proceedings of the 25th CDC, Athens 1986, pp. 192–197.

  20. H. Nijmeijer and W. Respondek, Dynamic Input-Output Decoupling of Nonlinear Control Systems, Memo No. 575, Technical University, Twente, 1986.

    Google Scholar 

  21. H. Nijmeijer and J. M. Schumacher, Zeros at infinity for affine nonlinear control systems,IEEE Trans. Automat. Control,30 (1985), 566–573.

    Article  MathSciNet  Google Scholar 

  22. L. M. Silverman, Inversion of multivariable linear systems,IEEE Trans. Automat. Control,14 (1969), 270–276.

    Article  Google Scholar 

  23. L. M. Silverman and A. Kitapçi, System structure at infinity,Systems Control Lett.,3 (1983), 123–131.

    Article  MathSciNet  Google Scholar 

  24. S. N. Singh, A modified algorithm for invertibility in nonlinear systems,IEEE Trans. Automat. Control,26 (1981), 595–598.

    Article  MathSciNet  Google Scholar 

  25. A. I. G. Vardulakis, On infinite zeros,Internat. J. Control,32 (1980), 849–866.

    MathSciNet  Google Scholar 

  26. A. I. G. Vardulakis, D. J. N. Limebeer, and N. Karcanias, Structure and Smith MacMillan form of a rational matrix at infinity,Internat. J. Control,35 (1982), 701–725.

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Laboratoire d’Automatique de Nantes, Unité Associée au C.N.R.S., E.N.S.M., 1 rue de la Noë, 44072, Nantes Cedex 03, France

    Claude H. Moog

Authors
  1. Claude H. Moog
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Moog, C.H. Nonlinear decoupling and structure at infinity. Math. Control Signal Systems 1, 257–268 (1988). https://doi.org/10.1007/BF02551287

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02551287

Key words

Search

Navigation