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Observability, Interpolation and Related Topics

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Computation and Control

Part of the book series: Progress in Systems and Control Theory ((PSCT,volume 1))

Abstract

In this paper some of the relations between the observability and identification in linear systems theory and the classical problems of interpolation and approximation will be examined. These problems are all classical, but it appears that a certain amount of insight can be gained by the cross fertilization of areas. There are many papers in this volume that are related to particular instances of the problems here proposed. When possible the reader will be referred to these papers for details.

Supported in part by NSA grant #MDA904-85-H0009 and NASA Grant #NAG282

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References

  1. Akhiezer, N.L., The classical moment problem and some related questions in analysis, Hafner Publishing Company, New York, 1965.

    MATH  Google Scholar 

  2. G. Ammar, W. Dayawansa and C. Martin, Exponential interpolation: theory and numerical algorithms, submitted.

    Google Scholar 

  3. G. Birkhoff, Boundary value and expansion problems of ordinary linear differential equations, Tran. Amer. Math. Soc, 9, 1908, 373–395.

    Article  MathSciNet  MATH  Google Scholar 

  4. C. Byrnes, W. Dayawansa and C. Martin, On the topology and geometry of universally observable systems, Proceedings of the 26th IEEE Conference on Decision and Control, 1987, Los Angeles, CA: 1987.

    Google Scholar 

  5. Gantmacher, F.R., Matrix theory, Vol 1, Chelsea Publishing Company, New York, 1977.

    Google Scholar 

  6. Gautschi, W., On generating orthogonal polynomials, SIAM J. Sei. Stat. Comput., 3, 1982, 289–317.

    Article  MathSciNet  MATH  Google Scholar 

  7. D. Gilliam, Z. Li, and C. Martin, Discrete observability of the heat equation on bounded domains, International Journal of Control, 48, (1988), 755–780.

    Article  MathSciNet  MATH  Google Scholar 

  8. D. Gilliam and C. Martin, Discrete observability and dirichlet series, System and Control Letters, 9, (1987), 345–348.

    Article  MathSciNet  MATH  Google Scholar 

  9. D. Gilliam, B. Mair and C. Martin, Observability and inversion for the heat equation, in Linear Circuits, Systems and Signal Processing: Theory and Application, C. Byrnes, C. Martin, R. Saeks (eds.). Amsterdam: North Holland Publishing Company, 1988, 363–370.

    Google Scholar 

  10. D. Gilliam, B. Mair and C. Martin, An inverse convolution method for regular parabolic equations, submitted.

    Google Scholar 

  11. D. Gilliam, B. Mair and C. Martin, A convolution inversion method for inverse heat conduction problems, Mathematical System Theory, 21, (1988), 49–60.

    Article  MathSciNet  MATH  Google Scholar 

  12. Hilderbrand, F., Introduction to numerical analysis, McGraw-Hill, New York, 1956.

    Google Scholar 

  13. I. Iakovidis, C.Martin and S. Xie, Observability and inverse problems arising in electrocardiography, this volume.

    Google Scholar 

  14. R. Kalman, Lectures on controllability and observability, C.I.M.E., Bologna, 1968.

    Google Scholar 

  15. D. McMahon, An example of a universally observable system, System and Control Letters, 8, 1987, pp 247–248.

    Article  MathSciNet  MATH  Google Scholar 

  16. C. Martin and J. Smith, Approximation, Interpolation and Sampling. In Differential Geometry: The interface between pure and applied mathematics, W. Shadwick, M. Luksic, and C. Martin (eds.) Contemporary Mathematics Series. Providence, RI: American Mathematical Society, 1987, 227–251

    Google Scholar 

  17. C. Martin and M. Stamp, Construction of polynomials over finite fields, this volume.

    Google Scholar 

  18. C. Martin and M. Stamp, Classification and realization of pseudorandom number generators, to appear, System and Control Letters.

    Google Scholar 

  19. C. Martin and D. I. Wallace, Observability and transcendental number theory, submitted.

    Google Scholar 

  20. A. B. Nemeth, Conjugate point classification with application to chebyshev systems, Rev. Anal. Numer. Theorie Approximation, 1974, 3, 73–78.

    MathSciNet  Google Scholar 

  21. de Prony,R., Essai experimental et analytique, J. Ecole Polytech. (Paris), 1, 1795, 24–76.

    Google Scholar 

  22. S. Kuo, D. Elliott and T.J. Tarn, Observability of nonlinear systems, Information and Control, 22, 1973, 89–99.

    Article  MathSciNet  Google Scholar 

  23. D. Wallace, Observability, predictability and chaos, this volume.

    Google Scholar 

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© 1989 Birkhäuser Boston

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Martin, C.F. (1989). Observability, Interpolation and Related Topics. In: Computation and Control. Progress in Systems and Control Theory, vol 1. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-3704-4_15

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  • DOI: https://doi.org/10.1007/978-1-4612-3704-4_15

  • Publisher Name: Birkhäuser Boston

  • Print ISBN: 978-0-8176-3438-4

  • Online ISBN: 978-1-4612-3704-4

  • eBook Packages: Springer Book Archive

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