On the genericity of the observability of controlled discrete-time systems
ESAIM: Control, Optimisation and Calculus of Variations, Tome 11 (2005) no. 2, pp. 161-179.

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

DOI : 10.1051/cocv:2005001
Classification : 57R40, 93B07, 93B27, 93C55
Mots clés : observability, nonlinear systems, discrete-time systems, transversality theory
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Ammar, Sabeur; Vivalda, Jean-Claude. On the genericity of the observability of controlled discrete-time systems. ESAIM: Control, Optimisation and Calculus of Variations, Tome 11 (2005) no. 2, pp. 161-179. doi : 10.1051/cocv:2005001. http://www.numdam.org/articles/10.1051/cocv:2005001/

[1] R. Abraham and J.W. Robbin, Transversal Mappings and Flows. W. A. Benjamin, New York (1967). | MR | Zbl

[2] D. Aeyels, Generic observability of differentiable systems. SIAM J. Control Optim. 19 (1981) 595-603. | MR | Zbl

[3] J.-P. Gauthier, H. Hammouri and I. Kupka, Observers for nonlinear systems. In Proc. of the IEEE 30th CDC (1991) 1483-1489.

[4] J.-P. Gauthier and I. Kupka, Observability and observers for nonlinear systems. SIAM J. Control Optim. 32 (1994) 975-994. | MR | Zbl

[5] J.-P. Gauthier and I. Kupka, Observability for systems with more outputs than inputs and asymptotic observers. Math. Zeitschrift 223 (1996) 47-78. | MR | Zbl

[6] J.P. Gauthier and I. Kupka, Deterministic observation: theory and applications. Cambridge: Cambridge University Press (2002). | MR | Zbl

[7] M. Golubitsky and V. Guillemin, Stable Mappings and Their Singularities. Springer-Verlag, New York (1986). | Zbl

[8] J. Stark, Delay embedding for forced systems - I. Deterministic forcing. J. Nonlinear Sci. 9 (1999) 255-332. | Zbl

[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).

[10] F. Takens, Detecting strange attractors in turbulence. No. 898 in Lect. Notes Math. Springer-Verlag, Coventry (1981). | MR | Zbl

[11] J.-C. Vivalda, On the genericity of the observability of uncontrolled discrete nonlinear systems. SIAM J. Control Optim. 42 (2003). | MR

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