Nonlinear observers for locally uniformly observable systems
ESAIM: Control, Optimisation and Calculus of Variations, Tome 9 (2003), pp. 353-370.

This paper deals with the observability analysis and the observer synthesis of a class of nonlinear systems. In the single output case, it is known [4, 5, 6] that systems which are observable independently of the inputs, admit an observable canonical form. These systems are called uniformly observable systems. Moreover, a high gain observer for these systems can be designed on the basis of this canonical form. In this paper, we extend the above results to multi-output uniformly observable systems. Corresponding canonical forms are presented and sufficient conditions which permit the design of constant and high gain observers for these systems are given.

DOI : https://doi.org/10.1051/cocv:2003017
Classification : 37N35,  93Bxx
Mots clés : nonlinear systems, uniform observability, nonlinear observer
@article{COCV_2003__9__353_0,
author = {Hammouri, Hassan and Farza, M.},
title = {Nonlinear observers for locally uniformly observable systems},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {353--370},
publisher = {EDP-Sciences},
volume = {9},
year = {2003},
doi = {10.1051/cocv:2003017},
zbl = {1063.93012},
mrnumber = {1966538},
language = {en},
url = {http://www.numdam.org/articles/10.1051/cocv:2003017/}
}
TY  - JOUR
AU  - Hammouri, Hassan
AU  - Farza, M.
TI  - Nonlinear observers for locally uniformly observable systems
JO  - ESAIM: Control, Optimisation and Calculus of Variations
PY  - 2003
DA  - 2003///
SP  - 353
EP  - 370
VL  - 9
PB  - EDP-Sciences
UR  - http://www.numdam.org/articles/10.1051/cocv:2003017/
UR  - https://zbmath.org/?q=an%3A1063.93012
UR  - https://www.ams.org/mathscinet-getitem?mr=1966538
UR  - https://doi.org/10.1051/cocv:2003017
DO  - 10.1051/cocv:2003017
LA  - en
ID  - COCV_2003__9__353_0
ER  - 
Hammouri, Hassan; Farza, M. Nonlinear observers for locally uniformly observable systems. ESAIM: Control, Optimisation and Calculus of Variations, Tome 9 (2003), pp. 353-370. doi : 10.1051/cocv:2003017. http://www.numdam.org/articles/10.1051/cocv:2003017/

[1] G. Besançon and H. Hammouri, On uniform observation of non uniformly observable systems. Systems Control Lett. 29 (1996) 9-19. | MR 1416747 | Zbl 0866.93013

[2] G. Besançon and H. Hammouri, On observer design for interconnected systems. J. Math. Systems Estim. Control 8 (1998). | MR 1650082 | Zbl 0918.93007

[3] G. Bornard and H. Hammouri, A high gain observer for a class of uniformly observable systems, in Proc. 30th IEEE Conference on Decision and Control Brighton 122 (1991) 176-192. | Zbl 0864.93018

[4] J.P. Gauthier and G. Bornard, Observability for any u(t) of a class of nonlinear systems. IEEE Trans. Automat. Control 26 (1981) 922-926. | MR 635851 | Zbl 0553.93014

[5] J.P. Gauthier, H. Hammouri and S. Othman, A simple observer for nonlinear systems - Application to bioreactors. IEEE Trans. Automat. Control 37 (1992) 875-880. | MR 1164571 | Zbl 0775.93020

[6] J.P. Gauthier and I.A.K. Kupka, Observability and observers for nonlinear systems. SIAM J. Control Optim. 32 (1994) 975-994. | MR 1280224 | Zbl 0802.93008

[7] J.P. Gauthier and I.A.K. Kupka, Observability for systems with more outputs than inputs. Math. Z. 223 (1996) 47-78. | EuDML 174910 | MR 1408862 | Zbl 0863.93008

[8] J.P. Gauthier and I.A.K. Kupka, Deterministic Observation Theory and Applications. Cambridge University Press (2001). | MR 1862985 | Zbl 0990.93001

[9] R. Hermann and A.J. Krener, Nonlinear controllability and observability. IEEE Trans. Automat. Control 22 (1977) 728-740. | MR 476017 | Zbl 0396.93015

[10] A. Isidori, Nonlinear control systems: An introducion, Vol. 72. Springer, Berlin (1985). | Zbl 0569.93034

[11] A.J. Krener and A. Isidori, Linearization by output injection and nonlinear observers. System Control Lett. 3 (1983) 47-52. | MR 713426 | Zbl 0524.93030

[12] A.J. Krener and W. Respondek, Nonlinear observers with linealizable error dynamics. SIAM J. Control Optim. 23 (1985) 197-216. | MR 777456 | Zbl 0569.93035

[13] H.J. Sussman, Single-input observability of continuous-time systems. Math. System Theory 12 (1979) 371-393. | MR 541865 | Zbl 0422.93019

[14] F.E. Thau, Observing the state of nonlinear dynamics systems. Int. J. Control 17 (1973) 471-479. | Zbl 0249.93006

[15] D. Williamson, Observability of bilinear systems, with application to biological control. Automatica 32 (1977) 143-254. | Zbl 0351.93008

Cité par Sources :