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ArticleOriginal scientific text

Title

Genericity of observability and the existence of asymptotic observers

Authors 1, 2

Affiliations

  1. Institut Universitaire de France, INSA de Rouen, Department of Mathematics, LMI, BP 08, Place Emile Blondel, 76131 Mont-Saint-Aignan, France
  2. Department of Mathematics, University of Toronto, 100, St Georges Street, Toronto, Ontario, M5S 1A1

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.

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Banach Center Publications
1995/32/1
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Pages:
227-244
Main language of publication
English
Published
1995
Exact and natural sciences