Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-27T07:59:38.795Z Has data issue: false hasContentIssue false

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

Published online by Cambridge University Press:  15 March 2005

Sabeur Ammar
Affiliation:
Inria-Lorraine & UMR CNRS 7122 – ISGMP Bâtiment A, Université de Metz, Ile du Saulcy, 57 045 Metz Cedex 01, France; ammar@loria.fr; vivalda@loria.fr
Jean-Claude Vivalda
Affiliation:
Inria-Lorraine & UMR CNRS 7122 – ISGMP Bâtiment A, Université de Metz, Ile du Saulcy, 57 045 Metz Cedex 01, France; ammar@loria.fr; vivalda@loria.fr
Get access

Abstract

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

Type
Research Article
Copyright
© EDP Sciences, SMAI, 2005

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

R. Abraham and J.W. Robbin, Transversal Mappings and Flows. W. A. Benjamin, New York (1967).
Aeyels, D., Generic observability of differentiable systems. SIAM J. Control Optim. 19 (1981) 595-603. CrossRef
J.-P. Gauthier, H. Hammouri and I. Kupka, Observers for nonlinear systems. In Proc. of the IEEE 30th CDC (1991) 1483-1489.
Gauthier, J.-P. and Kupka, I., Observability and observers for nonlinear systems. SIAM J. Control Optim. 32 (1994) 975-994. CrossRef
Gauthier, J.-P. and Kupka, I., Observability for systems with more outputs than inputs and asymptotic observers. Math. Zeitschrift 223 (1996) 47-78. CrossRef
J.P. Gauthier and I. Kupka, Deterministic observation: theory and applications. Cambridge: Cambridge University Press (2002).
M. Golubitsky and V. Guillemin, Stable Mappings and Their Singularities. Springer–Verlag, New York (1986).
Stark, J., Delay embedding for forced systems – I. Deterministic forcing. J. Nonlinear Sci. 9 (1999) 255-332. CrossRef
J. Stark, D.S. Broomhead, M.E. Davies and J. Huke, Delay embedding for forced systems – II. Stochastic forcing. J. Nonlinear Sci. (to appear).
F. Takens, Detecting strange attractors in turbulence. No. 898 in Lect. Notes Math. Springer-Verlag, Coventry (1981).
J.-C. Vivalda, On the genericity of the observability of uncontrolled discrete nonlinear systems. SIAM J. Control Optim. 42 (2003).