The Input-Output Decoupling Problem: Geometric Considerations

Chapter

Abstract

In the previous chapter we have given an analytic approach to the input-output decoupling problem for analytic systems.

Keywords

Nonlinear System Geometric Consideration Nonlinear Control System Satisfying Assumption Output Block 
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References

  1. [BM70].
    G. Basile and G. Marro. A state space approach to noninteracting controls. Ricerche di Automatica, 1:68–77, 1970.Google Scholar
  2. [Che88].
    D. Cheng. Design for noninteracting decomposition of nonlinear systems. IEEE Trans. Aut. Contr., AC-33:1070–1074, 1988.Google Scholar
  3. [DBGM89].
    M.D. Di Benedetto, J.W. Grizzle, and C.H. Moog. Rank invariants of nonlinear systems. SIAM J. Contr. Optimiz., 27:658–672, 1989.Google Scholar
  4. [Dio83].
    J.M. Dion. Feedback block decoupling and infinite structure of linear systems. Int. J. Contr., 37:521–533, 1983.Google Scholar
  5. [DLM83].
    J. Descusse, J.F. Lafay, and M. Malabre. On the structure at infinity of blockdecouplable systems: the general case. IEEE Trans. Aut. Contr., AC-28:1115–1118, 1983.Google Scholar
  6. [GDBM87].
    J.W. Grizzle, M.D. Di Benedetto, and C.H. Moog. Computing the differential output rank of a nonlinear system. In Proc. 26th IEEE Conf. Decision Control, Los Angeles, pages 142–145, 1987.Google Scholar
  7. [Hau76].
    M.L.J. Hautus. The formal Laplace transform for smooth linear systems. In Mathematical Systems Theory, volume 131 of Lect. Notes Econ. Math. Syst., pages 29–47. Springer, Berlin, 1976.Google Scholar
  8. [HG86].
    I.J. Ha and E.G. Gilbert. A complete characterization of decoupling control laws for a general class of nonlinear systems. IEEE Trans. Automat. Contr., AC-31:823–830, 1986.Google Scholar
  9. [IG88].
    A. Isidori and J.W. Grizzle. Fixed modes and nonlinear noninteracting control with stability. IEEE Trans. Aut. Contr., AC-33:907–914, 1988.Google Scholar
  10. [IKGGM81].
    A. Isidori, A.J. Krener, C. Gori-Giorgi, and S. Monaco. Nonlinear decoupling via feedback: a differential geometric approach. IEEE Trans. Aut. Contr., AC-26:331–345, 1981.Google Scholar
  11. [Isi83a].
    A. Isidori. Formal infinite zeros for nonlinear systems. In Proc. 22-nd Conf. Decision Control, San Antonio, pages 647–653, 1983.Google Scholar
  12. [Isi83b].
    A. Isidori. Nonlinear feedback, structure at infinity and the input-output linearization problem. In Mathematical Theory of Networks and Systems, volume 58 of Lect. Notes Contr. Inf. Sci., pages 473–493. Springer, Berlin, 1983.Google Scholar
  13. [Isi86b].
    A. Isidori. Control of nonlinear systems via dynamic state-feedback. In M. Fliess and M. Hazewinkel, editors, Algebraic and Geometric Methods in Nonlinear Control Theory, volume 29 of Math. Appl., pages 121–146. Reidel, Dordrecht, 1986.Google Scholar
  14. [Mal82].
    M. Malabre. Structure `a l’infini des triplets invariants: application `a la poursuite parfaite de mod`ele. In A. Bensoussan and J.L. Lions, editors, Analysis and Optimization of Systems, volume 44 of Lect. Notes Contr. Inf. Sci., pages 43–53. Springer, Berlin, 1982.Google Scholar
  15. [MG88].
    C.H. Moog and J.W. Grizzle. D’ecouplage non lin’eaire vu de l’alg`ebre lin’eaire. C.R. Acad. Sci. Paris, S´erie I, t.307:497–500, 1988.Google Scholar
  16. [Mor73].
    A.S. Morse. Structural invariants of linear multivariable systems. SIAM J. Contr. Optimiz., 11:446–465, 1973.Google Scholar
  17. [MW71].
    A.S. Morse and W.M. Wonham. Status of noninteracting control. IEEE Trans. Aut. Contr., AC-16:568–581, 1971.Google Scholar
  18. [Nij83].
    H. Nijmeijer. Feedback decomposition of nonlinear control systems. IEEE Trans. Aut. Contr., AC-28:861–862, 1983.Google Scholar
  19. [Nij85].
    H. Nijmeijer. Zeros at infinity for nonlinear systems, what are they and what are they good for? In B. Jakubczyk, W. Respondek, and K. Tcho’n, editors, Geometric Theoryof Nonlinear Control Systems, volume 70, pages 105–130. Scientific Paper of the Institute of Technical Cybernetics of the Technical University of Wroclaw, Poland, 1985Google Scholar
  20. [Nij86].
    H. Nijmeijer. On the input-output decoupling of nonlinear systems. In M. Fliess and M. Hazewinkel, editors, Algebraic and Geometric Methods in Nonlinear Control Theory, volume 29 of Math. Appl., pages 101–119. Reidel, Dordrecht, 1986.Google Scholar
  21. [NS83].
    H. Nijmeijer and J.M. Schumacher. The regular local noninteracting control problem for nonlinear control systems. In Proc. 22-nd IEEE Conf. Decision Control, San Antonio, pages 388–392, 1983.Google Scholar
  22. [NS85a].
    H. Nijmeijer and J.M. Schumacher. On the inherent integration structure of nonlinear systems. IMA J. Math. Contr. Inf., 2:87–107, 1985.Google Scholar
  23. [NS85b].
    H. Nijmeijer and J.M. Schumacher. Zeros at infinity for affine nonlinear control systems. IEEE Trans. Aut. Contr., AC-30:566–573, 1985.Google Scholar
  24. [NS86].
    H. Nijmeijer and J.M. Schumacher. The regular local noninteracting control problem for nonlinear control systems. SIAM J. Contr. Optimiz., 24:1232–1245, 1986.Google Scholar
  25. [Ros70].
    H.H. Rosenbrock. State space and Multivariable Theory. Wiley, New York, 1970.Google Scholar
  26. [WM70].
    W.M.Wonham and A.S. Morse. Decoupling and pole assignment in linear multivariable systems: a geometric approach. SIAM J. Contr. Optimiz., 8:1–18, 1970.Google Scholar
  27. [Won79].
    W.M. Wonham. Linear Multivariable Control: a Geometric Approach. Springer, Berlin, 2-nd edition, 1979.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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