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1995 | 32 | 1 | 227-244
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Genericity of observability and the existence of asymptotic observers

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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.
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  • Institut Universitaire de France, INSA de Rouen, Department of Mathematics, LMI, BP 08, Place Emile Blondel, 76131 Mont-Saint-Aignan, France
  • Department of Mathematics, University of Toronto, 100, St Georges Street, Toronto, Ontario, M5S 1A1
  • [A] D. Aeyels, Generic observability of differentiable systems, SIAM J. Control Optim. 19 (1981), 1-15.
  • [AR] R. Abraham and J. Robbin, Transversal Mappings and Flows, Benjamin, 1967.
  • [GHK] J. P. Gauthier, H. Hammouri and I. Kupka, Observers for nonlinear systems, IEEE CDC Conference, Brighton, 1991, 1483-1489.
  • [GHO] J. P. Gauthier, H. Hammouri and S. Othman, A simple observer for nonlinear systems, application to bioreactors, IEEE Trans. Automat. Control 37 (1992), 875-880.
  • [GK] J. P. Gauthier and I. Kupka, Observability and observers for nonlinear systems, SIAM J. Control Optim. 32 (1994), 975-995.
  • [HG1] H. Hammouri and J. P. Gauthier, Bilinearization up to output injection, Systems Control Letters 11 (1988), 139-149.
  • [HG2] H. Hammouri and J. P. Gauthier, Global time varying linearization up to output injection, SIAM J. Control 6 (1992), 1295-1310.
  • [HIR] M. W. Hirsch, Differential Topology, Springer, 1976.
  • [KI] A. Krener and A. Isidori, Linearization by output injection and nonlinear observers, Systems Control Letters 3 (1983), 47-52.
  • [KR] A. Krener and W. Respondek, Nonlinear observers with linearizable error dynamics, SIAM J. Control Optim. 23 (1985), 197-216.
  • [L] S. Łojasiewicz, Triangulation of semi-analytic sets, Ann. Scuola Norm. Sup. PISA, 1964, 449-474.
  • [LU] D. G. Luenberger, Observers for multivariable systems, IEEE Trans. Automat. Control 11 (1966), 190-197.
  • [S] H. Sussmann, Single input observability of continuous time systems, Math. Systems Theory 12 (1979), 263-284.
  • [T] F. Takens, Detecting strange attractors in turbulence, in: Dynamic Systems and Turbulence, Warwick 1980, Springer, Berlin, 1981, 366-381.
  • [TC] K. Tchon, On solvability of several affine systems, Systems Control Letters 4 (1984), 373-379.
  • [TOU] J. C. Tougeron, Idéaux de fonctions différentiables, Springer, 1972.
  • [WH] H. Whitney, Analytic extensions of differentiable functions defined in closed sets, Trans. Amer. Math. Soc. 36 (1934), 63-89.
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