Discrete-Time Nonlinear Control Systems

Chapter

Abstract

In the preceding chapters we have restricted ourselves to continuous-time nonlinear control systems, and their discrete-time counterparts have been ignored so far. Although most engineering applications are concerned with (physical) continuous time systems, discrete-time systems naturally occur in various situations. Most commonly discrete-time nonlinear systems appear as the discretization of continuous time nonlinear systems.

Keywords

Equilibrium Point State Feedback Librium Point Characteristic Number Static State Feedback 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [AHS84]
    K.J. Aström, P. Hagander, and J. Sternby. Zeros of sampled systems. Automatica, 20:31–38, 1984.Google Scholar
  2. [AJL+89]
    A. Arapostathis, B. Jakubczyk, H.G. Lee, S.I. Marcus, and E.D. Sontag. The effect of sampling on linear equivalence and feedback linearization. Systems Control Lett., 13:373–381, 1989.Google Scholar
  3. [Che84]
    C.T. Chen. Linear System Theory and Design. Holt, Rinehart and Winston, New York, 1984.Google Scholar
  4. [Fli86]
    M. Fliess. Esquisses pour une théorie des systèmes nonlinéaires en temps discret. In Rend. Sem. Mat. Univers. Politechnico Torino, pages 55–67, 1986.Google Scholar
  5. [FN81]
    M. Fliess and D. Normand-Cyrot. A group theoretic approach to discrete-time nonlinear controllability. In Proc. 20th. IEEE Conf. Decision Control, San Diego, pages 551–557, 1981.Google Scholar
  6. [GN86]
    J.W. Grizzle and H. Nijmeijer. Zeros at infinity for nonlinear discrete-time systems. Math. Syst. Th., 19:79–93, 1986.Google Scholar
  7. [Gri85a]
    J.W. Grizzle. Controlled invariance for discrete-time nonlinear systems with an application to the disturbance decoupling problem. IEEE Trans. Aut. Contr., AC-30:868–874, 1985.Google Scholar
  8. [Gri85b]
    J.W. Grizzle. Distributions invariantes commandées pour les systèmes nonlinéaires en temps discret. C.R. Acad. Sci. Paris, Série I, t.300:447–450, 1985.Google Scholar
  9. [Gri86a]
    J.W. Grizzle. Feedback linearization of discrete-time systems. In A. Bensoussan and J.L Lions, editors, Analysis and Optimization of Systems, volume 83 of Lect. Notes Contr. Inf. Sci., pages 273–281. Springer, Berlin, 1986.Google Scholar
  10. [Gri86b]
    J.W. Grizzle. Local input-output decoupling of discrete-time nonlinear systems. Int. J. Contr., 43:1517–1530, 1986.Google Scholar
  11. [GS88]
    J.W. Grizzle and M.H. Shor. Sampling, infinite zeros and decoupling of linear systems. Automatica, 24:387–396, 1988.Google Scholar
  12. [Jak87]
    B. Jakubczyk. Feedback linearization of discrete-time systems. Systems Control Lett., 9:411–416, 1987.Google Scholar
  13. [JN84]
    B. Jakubczyk and D. Normand-Cyrot. Orbites de pseudo-groupes de difféomorphismes et commandabilité des systèmes nonlinéaires en temps discret. C.R. Acad. Sci. Paris, Série I, t.298:257–260, 1984.Google Scholar
  14. [JS88]
    B. Jakubczyk and E.D. Sontag. Controllability of nonlinear discrete-time systems: a Liealgebraic approach. Report SYCON-88-09, Rutgers Center for Systems and Control, 1988.Google Scholar
  15. [Kot89]
    U. Kotta. The disturbance decoupling problem in nonlinear discrete time systems. In Preprints IFAC-Symposium Nonlinear Control Systems Design, Capri, Italy, pages 59–63, 1989.Google Scholar
  16. [LAM87]
    H.G. Lee, A. Arapostathis, and S.I. Marcus. On the linearization of discrete-time systems. Int. J. Contr., 45:1803–1822, 1987.Google Scholar
  17. [LM86]
    H.G. Lee and S.I. Marcus. Approximate and local linearizability of nonlinear discretetime systems. Int. J. Contr., 44:1103–1124, 1986.Google Scholar
  18. [LM87]
    H.G. Lee and S.I. Marcus. On input-output linearization of discrete-time nonlinear systems. Systems Control Lett., 8:249–260, 1987.Google Scholar
  19. [MN84a]
    S. Monaco and D. Normand-Cyrot. Invariant distributions for discrete time nonlinear systems. Systems Control Lett., 5:191–196, 1984.Google Scholar
  20. [MN84b]
    S.Monaco and D. Normand-Cyrot. Sur la commande non interactive des systèmes nonlin éaires en temps discret. In A. Bensoussan and J.L. Lions, editors, Analysis and Optimization of Systems, volume 63 of Lect. Notes Contr. Inf. Sci., pages 364–377. Springer, Berlin, 1984.Google Scholar
  21. [MN88]
    S. Monaco and D. Normand-Cyrot. Zero dynamics of sampled nonlinear systems. Systems Control Lett., 11:229–234, 1988.Google Scholar
  22. [MNI89]
    S. Monaco, D. Normand-Cyrot, and I. Isola. Nonlinear decoupling in discrete time. In Preprints IFAC-Symposium Nonlinear Control Systems Design, Capri, Italy, pages 48–55, 1989.Google Scholar
  23. [Nij82]
    H. Nijmeijer. Observability of autonomous discrete-time nonlinear systems, a geometric approach. Int. J. Contr., 36:867–874, 1982.Google Scholar
  24. [Nij87]
    H. Nijmeijer. Local (dynamic) input-output decoupling of discrete-time nonlinear systems IMA J. Math. Contr. Inf., 4:237–250, 1987.Google Scholar
  25. [Nij89a]
    H. Nijmeijer. On dynamic decoupling and dynamic path controllability in economic systems. J. Econ. Dyn. Contr., 13:21–39, 1989.Google Scholar
  26. [Nij89b]
    H. Nijmeijer. Remarks on the control of discrete-time nonlinear systems. In B. Jakubczyk, K. Malanowski, and W. Respondek, editors, Perspectives in control theory. Birkhauser, Boston, 1989.Google Scholar
  27. [Nor83]
    D. Normand-Cyrot. Théorie et pratique des systèmes nonlinéaires en temps discret. Thése de Doctorat d’Etat, Université de Paris Sud, Centre d’Orsay, 1983.Google Scholar
  28. [Son79]
    E.D. Sontag. Polynomial response maps. Springer, Berlin, 1979.Google Scholar
  29. [Son86]
    E.D. Sontag. An eigenvalue condition for sampled weak controllability of bilinear systems. Systems Control Lett., 7:313–316, 1986.Google Scholar

Copyright information

© Springer Science+Business Media New York 1990, Corrected printing 2016 1990

Authors and Affiliations

  1. 1.Dynamics and Control GroupEindhoven University of TechnologyEindhovenThe Netherlands
  2. 2.Johann Bernoulli Institute for Mathematics and Computer ScienceUniversity of GroningenGroningenThe Netherlands

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