Genericity of observability and the existence of asymptotic observers

J. Gauthier; I Kupka

Banach Center Publications (1995)

  • Volume: 32, Issue: 1, page 227-244
  • ISSN: 0137-6934

Abstract

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In this paper, we deal with the genericity of the observability property and the existence of asymptotic observers for nonlinear systems. In the case where the number of outputs is larger than the number of inputs and the state space is compact, we prove that observability in a very strong sense (more or less, observability for each sufficiently differentiable input) is generic. This is obtained by using standard (but not easy) transversality arguments. For the inputs that are bounded with their derivatives up to some order, we prove the generic existence of an asymptotic observer with arbitrary exponential decay of the error.

How to cite

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Gauthier, J., and Kupka, I. "Genericity of observability and the existence of asymptotic observers." Banach Center Publications 32.1 (1995): 227-244. <http://eudml.org/doc/262690>.

@article{Gauthier1995,
abstract = {In this paper, we deal with the genericity of the observability property and the existence of asymptotic observers for nonlinear systems. In the case where the number of outputs is larger than the number of inputs and the state space is compact, we prove that observability in a very strong sense (more or less, observability for each sufficiently differentiable input) is generic. This is obtained by using standard (but not easy) transversality arguments. For the inputs that are bounded with their derivatives up to some order, we prove the generic existence of an asymptotic observer with arbitrary exponential decay of the error.},
author = {Gauthier, J., Kupka, I},
journal = {Banach Center Publications},
keywords = {generic properties; observability; asymptotic observers},
language = {eng},
number = {1},
pages = {227-244},
title = {Genericity of observability and the existence of asymptotic observers},
url = {http://eudml.org/doc/262690},
volume = {32},
year = {1995},
}

TY - JOUR
AU - Gauthier, J.
AU - Kupka, I
TI - Genericity of observability and the existence of asymptotic observers
JO - Banach Center Publications
PY - 1995
VL - 32
IS - 1
SP - 227
EP - 244
AB - In this paper, we deal with the genericity of the observability property and the existence of asymptotic observers for nonlinear systems. In the case where the number of outputs is larger than the number of inputs and the state space is compact, we prove that observability in a very strong sense (more or less, observability for each sufficiently differentiable input) is generic. This is obtained by using standard (but not easy) transversality arguments. For the inputs that are bounded with their derivatives up to some order, we prove the generic existence of an asymptotic observer with arbitrary exponential decay of the error.
LA - eng
KW - generic properties; observability; asymptotic observers
UR - http://eudml.org/doc/262690
ER -

References

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  12. [LU] D. G. Luenberger, Observers for multivariable systems, IEEE Trans. Automat. Control 11 (1966), 190-197. 
  13. [S] H. Sussmann, Single input observability of continuous time systems, Math. Systems Theory 12 (1979), 263-284. Zbl0422.93019
  14. [T] F. Takens, Detecting strange attractors in turbulence, in: Dynamic Systems and Turbulence, Warwick 1980, Springer, Berlin, 1981, 366-381. 
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