# Nonlinear observers for locally uniformly observable systems

ESAIM: Control, Optimisation and Calculus of Variations (2010)

- Volume: 9, page 353-370
- ISSN: 1292-8119

## Access Full Article

top## Abstract

top## How to cite

topHammouri, Hassan, and Farza, M.. "Nonlinear observers for locally uniformly observable systems." ESAIM: Control, Optimisation and Calculus of Variations 9 (2010): 353-370. <http://eudml.org/doc/90700>.

@article{Hammouri2010,

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.
},

author = {Hammouri, Hassan, Farza, M.},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {Nonlinear systems; uniform observability; nonlinear observer.; nonlinear systems; nonlinear observer},

language = {eng},

month = {3},

pages = {353-370},

publisher = {EDP Sciences},

title = {Nonlinear observers for locally uniformly observable systems},

url = {http://eudml.org/doc/90700},

volume = {9},

year = {2010},

}

TY - JOUR

AU - Hammouri, Hassan

AU - Farza, M.

TI - Nonlinear observers for locally uniformly observable systems

JO - ESAIM: Control, Optimisation and Calculus of Variations

DA - 2010/3//

PB - EDP Sciences

VL - 9

SP - 353

EP - 370

AB -
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.

LA - eng

KW - Nonlinear systems; uniform observability; nonlinear observer.; nonlinear systems; nonlinear observer

UR - http://eudml.org/doc/90700

ER -

## References

top- G. Besançon and H. Hammouri, On uniform observation of non uniformly observable systems. Systems Control Lett.29 (1996) 9-19. Zbl0866.93013
- G. Besançon and H. Hammouri, On observer design for interconnected systems. J. Math. Systems Estim. Control 8 (1998). Zbl0918.93007
- 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. Zbl0864.93018
- J.P. Gauthier and G. Bornard, Observability for any u(t) of a class of nonlinear systems. IEEE Trans. Automat. Control26 (1981) 922-926. Zbl0553.93014
- J.P. Gauthier, H. Hammouri and S. Othman, A simple observer for nonlinear systems - Application to bioreactors. IEEE Trans. Automat. Control37 (1992) 875-880. Zbl0775.93020
- J.P. Gauthier and I.A.K. Kupka, Observability and observers for nonlinear systems. SIAM J. Control Optim.32 (1994) 975-994. Zbl0802.93008
- J.P. Gauthier and I.A.K. Kupka, Observability for systems with more outputs than inputs. Math. Z.223 (1996) 47-78. Zbl0863.93008
- J.P. Gauthier and I.A.K. Kupka, Deterministic Observation Theory and Applications. Cambridge University Press (2001). Zbl0990.93001
- R. Hermann and A.J. Krener, Nonlinear controllability and observability. IEEE Trans. Automat. Control22 (1977) 728-740. Zbl0396.93015
- A. Isidori, Nonlinear control systems: An introducion, Vol. 72. Springer, Berlin (1985).
- A.J. Krener and A. Isidori, Linearization by output injection and nonlinear observers. System Control Lett.3 (1983) 47-52. Zbl0524.93030
- A.J. Krener and W. Respondek, Nonlinear observers with linealizable error dynamics. SIAM J. Control Optim.23 (1985) 197-216. Zbl0569.93035
- H.J. Sussman, Single-input observability of continuous-time systems. Math. System Theory12 (1979) 371-393. Zbl0422.93019
- F.E. Thau, Observing the state of nonlinear dynamics systems. Int. J. Control17 (1973) 471-479. Zbl0249.93006
- D. Williamson, Observability of bilinear systems, with application to biological control. Automatica32 (1977) 143-254. Zbl0351.93008

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.