Skip to main content
SpringerLink
Log in
Book cover

Nonlinear Dynamical Control Systems pp 251–272Cite as

The Input-Output Decoupling Problem: Geometric Considerations

  • Chapter

  • 1974 Accesses

Abstract

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

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

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   109.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   139.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   139.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. G. Basile and G. Marro. A state space approach to noninteracting controls. Ricerche di Automatica, 1:68–77, 1970.

    Google Scholar 

  2. D. Cheng. Design for noninteracting decomposition of nonlinear systems. IEEE Trans. Aut. Contr., AC-33:1070–1074, 1988.

    Google Scholar 

  3. 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. J.M. Dion. Feedback block decoupling and infinite structure of linear systems. Int. J. Contr., 37:521–533, 1983.

    Google Scholar 

  5. 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. 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. 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. 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. 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. 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. A. Isidori. Formal infinite zeros for nonlinear systems. In Proc. 22-nd Conf. Decision Control, San Antonio, pages 647–653, 1983.

    Google Scholar 

  12. 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. 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. 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. 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. A.S. Morse. Structural invariants of linear multivariable systems. SIAM J. Contr. Optimiz., 11:446–465, 1973.

    Google Scholar 

  17. A.S. Morse and W.M. Wonham. Status of noninteracting control. IEEE Trans. Aut. Contr., AC-16:568–581, 1971.

    Google Scholar 

  18. H. Nijmeijer. Feedback decomposition of nonlinear control systems. IEEE Trans. Aut. Contr., AC-28:861–862, 1983.

    Google Scholar 

  19. 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, 1985

    Google Scholar 

  20. 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. 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. 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. 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. 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. H.H. Rosenbrock. State space and Multivariable Theory. Wiley, New York, 1970.

    Google Scholar 

  26. 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. W.M. Wonham. Linear Multivariable Control: a Geometric Approach. Springer, Berlin, 2-nd edition, 1979.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dynamics and Control Group, Eindhoven University of Technology, Den Dolech 2, 5600 MB, Eindhoven, The Netherlands

    Henk Nijmeijer

  2. Johann Bernoulli Institute for Mathematics and Computer Science, University of Groningen, 407 9700 AK, Groningen, The Netherlands

    Arjan van der Schaft

Authors
  1. Henk Nijmeijer
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Arjan van der Schaft
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Henk Nijmeijer .

Rights and permissions

Reprints and permissions

Copyright information

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

About this chapter

Cite this chapter

Nijmeijer, H., van der Schaft, A. (1990). The Input-Output Decoupling Problem: Geometric Considerations. In: Nonlinear Dynamical Control Systems. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-2101-0_9

Download citation

  • DOI: https://doi.org/10.1007/978-1-4757-2101-0_9

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4757-2102-7

  • Online ISBN: 978-1-4757-2101-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation