Linearization by completely generalized input-output injection

Virgilio López Morales; Franck Plestan; Alain Glumineau

Kybernetika (1999)

  • Volume: 35, Issue: 6, page [793]-802
  • ISSN: 0023-5954

Abstract

top
The problem addressed in this paper is the linearization of nonlinear systems by generalized input-output (I/O) injection. The I/O injection (called completely generalized I/O injection) depends on a finite number of time derivatives of input and output functions. The practical goal is the observer synthesis with linear error dynamics. The method is based on the I/O differential equation structure. Thus, the problem is solved as a realization one. A necessary and sufficient condition is proposed through a constructive algorithm and is based on the exterior differentiation.

How to cite

top

López Morales, Virgilio, Plestan, Franck, and Glumineau, Alain. "Linearization by completely generalized input-output injection." Kybernetika 35.6 (1999): [793]-802. <http://eudml.org/doc/33463>.

@article{LópezMorales1999,
abstract = {The problem addressed in this paper is the linearization of nonlinear systems by generalized input-output (I/O) injection. The I/O injection (called completely generalized I/O injection) depends on a finite number of time derivatives of input and output functions. The practical goal is the observer synthesis with linear error dynamics. The method is based on the I/O differential equation structure. Thus, the problem is solved as a realization one. A necessary and sufficient condition is proposed through a constructive algorithm and is based on the exterior differentiation.},
author = {López Morales, Virgilio, Plestan, Franck, Glumineau, Alain},
journal = {Kybernetika},
keywords = {linearization of nonlinear systems; input-output injection; exterior differentiation; I or O differential equation structure; observer synthesis; linearization of nonlinear systems; input-output injection; exterior differentiation; I or O differential equation structure; observer synthesis},
language = {eng},
number = {6},
pages = {[793]-802},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Linearization by completely generalized input-output injection},
url = {http://eudml.org/doc/33463},
volume = {35},
year = {1999},
}

TY - JOUR
AU - López Morales, Virgilio
AU - Plestan, Franck
AU - Glumineau, Alain
TI - Linearization by completely generalized input-output injection
JO - Kybernetika
PY - 1999
PB - Institute of Information Theory and Automation AS CR
VL - 35
IS - 6
SP - [793]
EP - 802
AB - The problem addressed in this paper is the linearization of nonlinear systems by generalized input-output (I/O) injection. The I/O injection (called completely generalized I/O injection) depends on a finite number of time derivatives of input and output functions. The practical goal is the observer synthesis with linear error dynamics. The method is based on the I/O differential equation structure. Thus, the problem is solved as a realization one. A necessary and sufficient condition is proposed through a constructive algorithm and is based on the exterior differentiation.
LA - eng
KW - linearization of nonlinear systems; input-output injection; exterior differentiation; I or O differential equation structure; observer synthesis; linearization of nonlinear systems; input-output injection; exterior differentiation; I or O differential equation structure; observer synthesis
UR - http://eudml.org/doc/33463
ER -

References

top
  1. Bestle D., Zeitz M., 10.1080/00207178308933084, Internat. J. Control 38 (1983), 419–431 (1983) MR0708425DOI10.1080/00207178308933084
  2. Birk J., Zeitz M., 10.1080/00207178808906138, Internat. J. Control 47 (1988), 1823–1836 (1988) MR0947071DOI10.1080/00207178808906138
  3. Chiasson J. N., 10.1109/87.273108, IEEE Trans. Systems Technology 2 (1994), 35–42 (1994) DOI10.1109/87.273108
  4. Diop S., Grizzle J. W., Moraal P. E., Stefanopoulou A., Interpolation and numerical differentiation for observer design, In: Proc. of American Control Conference 94, Evanston 1994, pp. 1329–1333 (1994) 
  5. Fliess M., 10.1109/9.58527, IEEE Trans. Automat. Control 35 (1990), 994–1001 (1990) Zbl0724.93010MR1065035DOI10.1109/9.58527
  6. Glumineau A., Moog C. H., Plestan F., 10.1109/9.489283, IEEE Trans. Automat. Control 41 (1996), 598–603 (1996) Zbl0851.93018MR1385333DOI10.1109/9.489283
  7. Hammouri H., Gauthier J. P., 10.1016/0167-6911(88)90088-6, Systems Control Lett. 11 (1988), 139–149 (1988) Zbl0648.93024MR0955483DOI10.1016/0167-6911(88)90088-6
  8. Keller H., 10.1080/00207178708934024, Internat. J. Control 46 (1987), 1915–1930 (1987) Zbl0634.93012MR0924264DOI10.1080/00207178708934024
  9. Krener A. J., Respondek W., 10.1137/0323016, Control Optim. 23 (1985), 197–216 (1985) MR0777456DOI10.1137/0323016
  10. López-M. V., Glumineau A., Further results on linearization of nonlinear systems by input output injection, In: Proc. of 36th IEEE Conference on Decision and Control, San Diego 1997 
  11. Marino R., 10.1109/9.58536, IEEE Trans. Automat. Control 35 (1990), 1054–1058 (1990) Zbl0729.93016MR1065044DOI10.1109/9.58536
  12. Marino R., Tomei P., 10.1016/0167-6911(91)90036-E, Systems Control Lett. 17 (1991), 115–121 (1991) Zbl0747.93069MR1120756DOI10.1016/0167-6911(91)90036-E
  13. Phelps A. R., 10.1137/0329030, SIAM J. Control Optim. 29 (1991), 516–534 (1991) Zbl0738.93032MR1089143DOI10.1137/0329030
  14. Plestan F., Cherki B., An observer for one flexible robot by an algebraic method, In: IFAC Workshop on New Trends in Design of Control Systems NTDCS’94, Smolenice 1994, pp. 41–46 (1994) 
  15. Plestan F., Glumineau A., 10.1016/S0167-6911(97)00025-X, Systems Control Lett. 31 (1997), 115–128 (1997) Zbl0901.93013MR1461807DOI10.1016/S0167-6911(97)00025-X
  16. Proychev T. Ph., Mishkov R. L., 10.1016/0005-1098(93)90145-J, Automatica 29 (1993), 495–498 (1993) Zbl0772.93017MR1211308DOI10.1016/0005-1098(93)90145-J
  17. Williamson D., 10.1016/0005-1098(77)90051-6, Automatica 13 (1977), 243–254 (1977) DOI10.1016/0005-1098(77)90051-6
  18. Xia X. H., Gao W. B., 10.1137/0327011, SIAM J. Control Optim. 27 (1989), 1, 199–216 (1989) MR0980230DOI10.1137/0327011

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.