Separation principle for nonlinear systems using a bilinear approximation

Mohamed Ali Hammami; Hamadi Jerbi

Kybernetika (2001)

  • Volume: 37, Issue: 5, page [565]-573
  • ISSN: 0023-5954

Abstract

top
In this paper, we study the local stabilization problem of a class of planar nonlinear systems by means of an estimated state feedback law. Our approach is to use a bilinear approximation to establish a separation principle.

How to cite

top

Hammami, Mohamed Ali, and Jerbi, Hamadi. "Separation principle for nonlinear systems using a bilinear approximation." Kybernetika 37.5 (2001): [565]-573. <http://eudml.org/doc/33551>.

@article{Hammami2001,
abstract = {In this paper, we study the local stabilization problem of a class of planar nonlinear systems by means of an estimated state feedback law. Our approach is to use a bilinear approximation to establish a separation principle.},
author = {Hammami, Mohamed Ali, Jerbi, Hamadi},
journal = {Kybernetika},
keywords = {nonlinear system; stabilization problem; feedback; bilinear approximation; nonlinear system; stabilization problem; feedback; bilinear approximation},
language = {eng},
number = {5},
pages = {[565]-573},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Separation principle for nonlinear systems using a bilinear approximation},
url = {http://eudml.org/doc/33551},
volume = {37},
year = {2001},
}

TY - JOUR
AU - Hammami, Mohamed Ali
AU - Jerbi, Hamadi
TI - Separation principle for nonlinear systems using a bilinear approximation
JO - Kybernetika
PY - 2001
PB - Institute of Information Theory and Automation AS CR
VL - 37
IS - 5
SP - [565]
EP - 573
AB - In this paper, we study the local stabilization problem of a class of planar nonlinear systems by means of an estimated state feedback law. Our approach is to use a bilinear approximation to establish a separation principle.
LA - eng
KW - nonlinear system; stabilization problem; feedback; bilinear approximation; nonlinear system; stabilization problem; feedback; bilinear approximation
UR - http://eudml.org/doc/33551
ER -

References

top
  1. Baccioti A., Boieri P., 10.1016/0167-6911(91)90008-3, Systems Control Lett. 16 (1991), 139–143 (1991) DOI10.1016/0167-6911(91)90008-3
  2. Boothby W., Marino R., 10.1016/0167-6911(89)90100-X, Systems Control Lett. 12 (1989), 87–92 (1989) Zbl0684.93062MR0979731DOI10.1016/0167-6911(89)90100-X
  3. Chabour R., Hammouri H., 10.1016/0893-9659(93)90137-C, Appl. Math. Lett. 6 (1993), 7–10 (1993) Zbl0774.93014MR1347745DOI10.1016/0893-9659(93)90137-C
  4. Chabour R., Sallet, G., Vivalda J. C., Stabilization of nonlinear two dimensional systems: a bilinear approach, Math. Control Signals Systems 9 (1996), 224–246 (1996) MR1358071
  5. Chabour R., Vivalda J. C., Stabilisation des systemes bilineaires dans le plan par une commande non reguliere, In: Proc. European Control Conference, ECC’91, Grenoble 1991, pp. 485–487 (1991) MR1113096
  6. Čelikovský S., 10.1016/0167-6911(90)90068-6, Systems Control Lett. 15 (1990), 433–439 (1990) Zbl0732.93012MR1084586DOI10.1016/0167-6911(90)90068-6
  7. Dayawansa W. P., Martin C. F., Knowles G., 10.1137/0328070, SIAM J. Control Optim. 28 (1990), 1321–1349 (1990) MR1075206DOI10.1137/0328070
  8. Gauthier J. P., Kupka I., 10.1109/9.182484, IEEE Trans. Automat. Control AC–37 (1992), 12, 1970–1974 (1992) Zbl0778.93102MR1200614DOI10.1109/9.182484
  9. Hahn W., Stability of Motion, Springer–Verlag, Berlin 1967 Zbl0189.38503MR0223668
  10. Hammami M. A., Stabilization of a class of nonlinear systems using an observer design, In: Proc. 32nd IEEE Conference on Decision and Control, San Antonio 1993, Vol. 3, pp. 1954–1959 (1993) 
  11. Hammami M. A., Jerbi H., 10.1016/0893-9659(94)90019-1, Appl. Math. Lett. 7 (1994), 4, 95–99 (1994) MR1350400DOI10.1016/0893-9659(94)90019-1
  12. Jerbi H., Quelques resultats sur la stabilization des systèmes non linéaires par estimation et retour d’état, Doctorat de l’université de Metz 1994 
  13. Jerbi H., Hammami M. A., Vivalda J. C., On the stabilization of homogeneous affine systems, In: 2nd IEEE M.S.N.D. Automat. Control, Chania 1994, pp. 319–326 (1994) 
  14. Massera J. L., 10.2307/1969955, Ann. of Math. 64 (1956), 182–206 (1956) MR0079179DOI10.2307/1969955
  15. Seibert P., Suarez R., 10.1016/0167-6911(90)90056-Z, Syst. Control Lett. 14 (1990), 347–352 (1990) Zbl0699.93073MR1052644DOI10.1016/0167-6911(90)90056-Z
  16. Vidyasagar M., 10.1109/TAC.1980.1102376, IEEE Trans. Automat. Control AC–25 (1980), 504–509 (1980) Zbl0429.93046MR0571757DOI10.1109/TAC.1980.1102376

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.