On nonlinear equivalence and backstepping observer
Kybernetika, Tome 37 (2001) no. 5, pp. 521-546
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

An observer design based on backstepping approach for a class of state affine systems is proposed. This class of nonlinear systems is determined via a constructive algorithm applied to a general nonlinear Multi Input–Multi Output systems. Some examples are given in order to illustrate the proposed methodology.
An observer design based on backstepping approach for a class of state affine systems is proposed. This class of nonlinear systems is determined via a constructive algorithm applied to a general nonlinear Multi Input–Multi Output systems. Some examples are given in order to illustrate the proposed methodology.
Classification : 93B07, 93B51, 93C10
Keywords: design; nonlinear system; multi-input–multi-output system; backstepping approach; state affine systems; nonlinear equivalence
@article{KYB_2001_37_5_a0,
     author = {Leon, J. de and Souleiman, I. and Glumineau, A. and Schreier, G.},
     title = {On nonlinear equivalence and backstepping observer},
     journal = {Kybernetika},
     pages = {521--546},
     year = {2001},
     volume = {37},
     number = {5},
     mrnumber = {1877072},
     zbl = {1265.93034},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2001_37_5_a0/}
}
TY  - JOUR
AU  - Leon, J. de
AU  - Souleiman, I.
AU  - Glumineau, A.
AU  - Schreier, G.
TI  - On nonlinear equivalence and backstepping observer
JO  - Kybernetika
PY  - 2001
SP  - 521
EP  - 546
VL  - 37
IS  - 5
UR  - http://geodesic.mathdoc.fr/item/KYB_2001_37_5_a0/
LA  - en
ID  - KYB_2001_37_5_a0
ER  - 
%0 Journal Article
%A Leon, J. de
%A Souleiman, I.
%A Glumineau, A.
%A Schreier, G.
%T On nonlinear equivalence and backstepping observer
%J Kybernetika
%D 2001
%P 521-546
%V 37
%N 5
%U http://geodesic.mathdoc.fr/item/KYB_2001_37_5_a0/
%G en
%F KYB_2001_37_5_a0
Leon, J. de; Souleiman, I.; Glumineau, A.; Schreier, G. On nonlinear equivalence and backstepping observer. Kybernetika, Tome 37 (2001) no. 5, pp. 521-546. http://geodesic.mathdoc.fr/item/KYB_2001_37_5_a0/

[1] Besançon G., Bornard, G., Hammouri H.: Observers synthesis for a class of nonlinear control systems. European J. Control (1996), 176–192 | DOI

[2] Busawon K., Farza, M., Hammouri H.: Observers’ synthesis for a class of nonlinear systems with application to state and parameter estimation in bioreactors. In: Proc. 36th IEEE Conference on Decision and Control, San Diego, California 1997

[3] Busawon K., Saif M.: An Observer for a class disturbance driven nonlinear systems. Appl. Math. Lett. 11 (1998), 6, 109–113 | DOI | MR

[4] Conte G., Moog C. H., Perdon A. M.: Nonlinear Control Systems – An algebraic setting. Springer–Verlag, Berlin 1999 | MR | Zbl

[5] Diop S.: Elimination in control theory. Math. Control Signals Systems 4 (1991), 17–32 | DOI | MR | Zbl

[6] Diop S., Fliess M.: On nonlinear observability. In: Proc. European Control Conference (ECC’91), Grenoble 1991

[7] Gauthier J. P., Bornard G.: Observability for any $u(t)$ of a class of nonlinear systems. IEEE Trans. Automat. Control 26 (1981), 922–926 | DOI | MR | Zbl

[8] Gauthier J. P., Kupka I.: Observability and observers for nonlinear systems. SIAM J. Control Optim. 32 (1994), 4, 974–994 | DOI | MR | Zbl

[9] Glumineau A., Moog C. H., Plestan F.: New algebro-geometric conditions for the linearization by input-output injection. IEEE Trans. Automat. Control 41 (1996), 598–603 | DOI | MR | Zbl

[10] Hammouri H., Gauthier: Global time varying linearization up to output injection. SIAM J. Control Optim. 30 (1992), 1295–1310 | DOI | MR | Zbl

[11] Hammouri H., Morales J. De Leon: Observer Synthesis for state affine systems. In: Proc. 29th IEEE Conference on Decision and Control, Honolulu 1990, pp. 784–785

[12] Kang W., Krener A. J.: Nonlinear asymptotic observer design: A backstepping approach. In: AFOSR Workshop on Dynamics Systems and Control, Pasadena, California 1998

[13] Krener A. J., Isidori A.: Linearization by output injection and nonlinear observers. Systems Control Lett. 3 (1983), 47–52 | MR | Zbl

[14] López–M. V., Morales, J. de Léon, Glumineau A.: Transformation of nonlinear systems into state affine control systems and observer synthesis. In: IFAC CSSC, Nantes 1998, pp. 771–776

[15] López–M. V., Plestan, F., Glumineau A.: Linearization by completely generalized input-output injection. Kybernetika 35 (1999), 6, 793–802 | MR

[16] Plestan F., Glumineau A.: Linearization by generalized input output injection. Systems Control Lett. 31 (1997), 115–128 | DOI | MR | Zbl

[17] Souleiman I., Glumineau A.: Constructive transformation of nonlinear systems into state affine MIMO form and nonlinear observers. Internat. J. Control. Submitted

[18] Nijmeijer H., (eds.) T. I. Fossen: New Directions in Nonlinear Observer Design (Lecture Notes in Control and Inform. Sciences 244). Springer–Verlag, Berlin 1999 | MR

[19] Schaft A. J. Van der: Representing a nonlinear state space system as a set of higher order differential equations in the inputs and outputs. Systems Control Lett. 12 (1989), 151–160 | DOI | MR

[20] Xia X. H., Gao W. B.: Nonlinear observer design by observer error linearization. SIAM J. Control Optim. 1 (1989), 199–216 | MR | Zbl