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.
Keywords: 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},
year = {2003},
publisher = {EDP Sciences},
volume = {9},
doi = {10.1051/cocv:2003017},
mrnumber = {1966538},
zbl = {1063.93012},
language = {en},
url = {https://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 SP - 353 EP - 370 VL - 9 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/cocv:2003017/ DO - 10.1051/cocv:2003017 LA - en ID - COCV_2003__9__353_0 ER -
%0 Journal Article %A Hammouri, Hassan %A Farza, M. %T Nonlinear observers for locally uniformly observable systems %J ESAIM: Control, Optimisation and Calculus of Variations %D 2003 %P 353-370 %V 9 %I EDP Sciences %U https://www.numdam.org/articles/10.1051/cocv:2003017/ %R 10.1051/cocv:2003017 %G en %F COCV_2003__9__353_0
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
[1] and, On uniform observation of non uniformly observable systems. Systems Control Lett. 29 (1996) 9-19. | Zbl | MR
[2] and, On observer design for interconnected systems. J. Math. Systems Estim. Control 8 (1998). | Zbl | MR
[3] and, 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
[4] and, Observability for any u(t) of a class of nonlinear systems. IEEE Trans. Automat. Control 26 (1981) 922-926. | Zbl | MR
[5] , and, A simple observer for nonlinear systems - Application to bioreactors. IEEE Trans. Automat. Control 37 (1992) 875-880. | Zbl | MR
[6] and, Observability and observers for nonlinear systems. SIAM J. Control Optim. 32 (1994) 975-994. | Zbl | MR
[7] and, Observability for systems with more outputs than inputs. Math. Z. 223 (1996) 47-78. | Zbl | MR | EuDML
[8] and, Deterministic Observation Theory and Applications. Cambridge University Press (2001). | Zbl | MR
[9] and, Nonlinear controllability and observability. IEEE Trans. Automat. Control 22 (1977) 728-740. | Zbl | MR
[10] , Nonlinear control systems: An introducion, Vol. 72. Springer, Berlin (1985). | Zbl
[11] and, Linearization by output injection and nonlinear observers. System Control Lett. 3 (1983) 47-52. | Zbl | MR
[12] and, Nonlinear observers with linealizable error dynamics. SIAM J. Control Optim. 23 (1985) 197-216. | Zbl | MR
[13] , Single-input observability of continuous-time systems. Math. System Theory 12 (1979) 371-393. | Zbl | MR
[14] , Observing the state of nonlinear dynamics systems. Int. J. Control 17 (1973) 471-479. | Zbl
[15] , Observability of bilinear systems, with application to biological control. Automatica 32 (1977) 143-254. | Zbl
Cité par Sources :
