On the genericity of the observability of controlled discrete-time systems

Sabeur Ammar; Jean-Claude Vivalda

ESAIM: Control, Optimisation and Calculus of Variations (2005)

  • Volume: 11, Issue: 2, page 161-179
  • ISSN: 1292-8119

Abstract

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In this paper, we prove the genericity of the observability for discrete-time systems with more outputs than inputs.

How to cite

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Ammar, Sabeur, and Vivalda, Jean-Claude. "On the genericity of the observability of controlled discrete-time systems." ESAIM: Control, Optimisation and Calculus of Variations 11.2 (2005): 161-179. <http://eudml.org/doc/244706>.

@article{Ammar2005,
abstract = {In this paper, we prove the genericity of the observability for discrete-time systems with more outputs than inputs.},
author = {Ammar, Sabeur, Vivalda, Jean-Claude},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {observability; nonlinear systems; discrete-time systems; transversality theory; Observability},
language = {eng},
number = {2},
pages = {161-179},
publisher = {EDP-Sciences},
title = {On the genericity of the observability of controlled discrete-time systems},
url = {http://eudml.org/doc/244706},
volume = {11},
year = {2005},
}

TY - JOUR
AU - Ammar, Sabeur
AU - Vivalda, Jean-Claude
TI - On the genericity of the observability of controlled discrete-time systems
JO - ESAIM: Control, Optimisation and Calculus of Variations
PY - 2005
PB - EDP-Sciences
VL - 11
IS - 2
SP - 161
EP - 179
AB - In this paper, we prove the genericity of the observability for discrete-time systems with more outputs than inputs.
LA - eng
KW - observability; nonlinear systems; discrete-time systems; transversality theory; Observability
UR - http://eudml.org/doc/244706
ER -

References

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  1. [1] R. Abraham and J.W. Robbin, Transversal Mappings and Flows. W. A. Benjamin, New York (1967). Zbl0171.44404MR240836
  2. [2] D. Aeyels, Generic observability of differentiable systems. SIAM J. Control Optim. 19 (1981) 595-603. Zbl0474.93016MR626654
  3. [3] J.-P. Gauthier, H. Hammouri and I. Kupka, Observers for nonlinear systems. In Proc. of the IEEE 30th CDC (1991) 1483-1489. 
  4. [4] J.-P. Gauthier and I. Kupka, Observability and observers for nonlinear systems. SIAM J. Control Optim. 32 (1994) 975-994. Zbl0802.93008MR1280224
  5. [5] J.-P. Gauthier and I. Kupka, Observability for systems with more outputs than inputs and asymptotic observers. Math. Zeitschrift 223 (1996) 47-78. Zbl0863.93008MR1408862
  6. [6] J.P. Gauthier and I. Kupka, Deterministic observation: theory and applications. Cambridge: Cambridge University Press (2002). Zbl0990.93001MR1862985
  7. [7] M. Golubitsky and V. Guillemin, Stable Mappings and Their Singularities. Springer–Verlag, New York (1986). Zbl0434.58001
  8. [8] J. Stark, Delay embedding for forced systems – I. Deterministic forcing. J. Nonlinear Sci. 9 (1999) 255-332. Zbl0985.37098
  9. [9] J. Stark, D.S. Broomhead, M.E. Davies and J. Huke, Delay embedding for forced systems – II. Stochastic forcing. J. Nonlinear Sci. (to appear). Zbl0896.93019
  10. [10] F. Takens, Detecting strange attractors in turbulence. No. 898 in Lect. Notes Math. Springer-Verlag, Coventry (1981). Zbl0513.58032MR654900
  11. [11] J.-C. Vivalda, On the genericity of the observability of uncontrolled discrete nonlinear systems. SIAM J. Control Optim. 42 (2003). Zbl1168.93316MR2044807

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