Abstract
The aim of this work is to generalize to the case of weighted L 2 spaces some results about L 2 approximation by analytic and rational functions which are useful to perform the identification of unknown transfer functions of stable (linear causal time-invariant) systems from incomplete frequency data.
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Alpay, D., Baratchart, L. and Leblond, J. (1993) Some extremal problems linked with identification from partial frequency data. In J.L. Lions, R.F. Curtain, A. Bensoussan, editor, 10th conference on analysis and optimization of systems, Sophia-Antipolis 1992, L.N. C.I.S., Springer-Verlag, 185, 563–573.
Baratchart, L., Cardelli, M. and Olivi, M. (1991) Identification and rational L 2 approximation: a gradient algorithm. Automatica, 27 (2): 413–418.
Baratchart, L. and Leblond, J. (1993) Characterization of solutions to a class of bounded extremal problems in L2. Unpublished.
Baratchart, L., Leblond, J. and Partington, J.R. (1994) Hardy approximation to Lr functions on subsets of the circle. INRIA research report 2377.
Baratchart, L., Olivi, M. and Wielonsky, F. (1992) On a rational approximation problem in the real hardy space H2. Theoretical Computer Science, 94: 175–197.
Cardelli, M. and Saff, E.B. (1992) An algorithm for a certain type of rational approximation in Hz. Unpublished.
Garnett, J.B. (1981) Bounded analytic functions. Academic Press.
Hoffman, K. (1988) Banach spaces of analytic functions. Dover.
Krein, M.G. and Nudel’man, P.Y. (1975) Approximation of Owl, w2) functions by minimum— energy transfer functions of linear systems. Problemy Peredachi Informatsii, 11(2):37–60. English translation.
Leblond, J.and Olivi, M. (1995) Hardy approximation in weighted L2 spaces of an arc. In preparation.
Ljung, L. (1987) System identification: Theory for the user. Prentice—Hall.
Patil, D.J. (1972) Representation of H’ functions. Bull. A.M.S., 78 (4).
Szegö, G. (1939) Orthogonal polynomials. Col. Pub. A.M.S, 23.
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© 1996 Springer Science+Business Media Dordrecht
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Leblond, J., Olivi, M. (1996). Weighted H 2 approximation of transfer functions. In: Doležal, J., Fidler, J. (eds) System Modelling and Optimization. IFIP — The International Federation for Information Processing. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-34897-1_9
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DOI: https://doi.org/10.1007/978-0-387-34897-1_9
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