Nonlinear observers for locally uniformly observable systems

Hassan Hammouri; M. Farza

ESAIM: Control, Optimisation and Calculus of Variations (2003)

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

Abstract

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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.

How to cite

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Hammouri, Hassan, and Farza, M.. "Nonlinear observers for locally uniformly observable systems." ESAIM: Control, Optimisation and Calculus of Variations 9 (2003): 353-370. <http://eudml.org/doc/245967>.

@article{Hammouri2003,
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, 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.},
author = {Hammouri, Hassan, Farza, M.},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {nonlinear systems; uniform observability; nonlinear observer},
language = {eng},
pages = {353-370},
publisher = {EDP-Sciences},
title = {Nonlinear observers for locally uniformly observable systems},
url = {http://eudml.org/doc/245967},
volume = {9},
year = {2003},
}

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
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, 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.
LA - eng
KW - nonlinear systems; uniform observability; nonlinear observer
UR - http://eudml.org/doc/245967
ER -

References

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  9. [9] R. Hermann and A.J. Krener, Nonlinear controllability and observability. IEEE Trans. Automat. Control 22 (1977) 728-740. Zbl0396.93015MR476017
  10. [10] A. Isidori, Nonlinear control systems: An introducion, Vol. 72. Springer, Berlin (1985). Zbl0569.93034
  11. [11] A.J. Krener and A. Isidori, Linearization by output injection and nonlinear observers. System Control Lett. 3 (1983) 47-52. Zbl0524.93030MR713426
  12. [12] A.J. Krener and W. Respondek, Nonlinear observers with linealizable error dynamics. SIAM J. Control Optim. 23 (1985) 197-216. Zbl0569.93035MR777456
  13. [13] H.J. Sussman, Single-input observability of continuous-time systems. Math. System Theory 12 (1979) 371-393. Zbl0422.93019MR541865
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