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Nonlinear observers for locally uniformly observable systems

Published online by Cambridge University Press:  15 September 2003

Hassan Hammouri  and
M. Farza
Hassan Hammouri
Affiliation:
LAGEP, UMR 5007 du CNRS, Université Lyon 1, ESCPE Lyon, bâtiment 308G, 43 boulevard du 11 novembre 1918, 69622 Villeurbanne Cedex, France; hammouri@lagep.cpe.fr.
M. Farza
Affiliation:
LAP, EA 2611, ISMRA, Université de Caen, 6 boulevard du Maréchal Juin, 14050 Caen Cedex, France.
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Abstract

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 [4-6] 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 systemsuniform observabilitynonlinear observer.
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 9 , January 2003 , pp. 353 - 370
Copyright
© EDP Sciences, SMAI, 2003

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References

Besançon, G. and Hammouri, H., On uniform observation of non uniformly observable systems. Systems Control Lett. 29 (1996) 9-19. CrossRef
G. Besançon and H. Hammouri, On observer design for interconnected systems. J. Math. Systems Estim. Control 8 (1998).
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.
Gauthier, J.P. and Bornard, G., Observability for any u(t) of a class of nonlinear systems. IEEE Trans. Automat. Control 26 (1981) 922-926. CrossRef
Gauthier, J.P., Hammouri, H. and Othman, S., A simple observer for nonlinear systems - Application to bioreactors. IEEE Trans. Automat. Control 37 (1992) 875-880. CrossRef
Gauthier, J.P. and Kupka, I.A.K., Observability and observers for nonlinear systems. SIAM J. Control Optim. 32 (1994) 975-994. CrossRef
Gauthier, J.P. and Kupka, I.A.K., Observability for systems with more outputs than inputs. Math. Z. 223 (1996) 47-78. CrossRef
J.P. Gauthier and I.A.K. Kupka, Deterministic Observation Theory and Applications. Cambridge University Press (2001).
Hermann, R. and Krener, A.J., Nonlinear controllability and observability. IEEE Trans. Automat. Control 22 (1977) 728-740. CrossRef
A. Isidori, Nonlinear control systems: An introducion, Vol. 72. Springer, Berlin (1985).
Krener, A.J. and Isidori, A., Linearization by output injection and nonlinear observers. System Control Lett. 3 (1983) 47-52. CrossRef
Krener, A.J. and Respondek, W., Nonlinear observers with linealizable error dynamics. SIAM J. Control Optim. 23 (1985) 197-216. CrossRef
Sussman, H.J., Single-input observability of continuous-time systems. Math. System Theory 12 (1979) 371-393. CrossRef
Thau, F.E., Observing the state of nonlinear dynamics systems. Int. J. Control 17 (1973) 471-479. CrossRef
Williamson, D., Observability of bilinear systems, with application to biological control. Automatica 32 (1977) 143-254.