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System approximation in the 2-norm

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Book cover Open Problems in Mathematical Systems and Control Theory

Part of the book series: Communications and Control Engineering ((CCE))

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Abstract

We present below a summary of some open problems in systems and control related to system approximation. For more details we refer to [3].

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References

  1. V.M. Adamjan, D.Z. Arov, and M.G. Krein, Analytic properties of Schmidt pairs for a Hankel operator and the generalized Schur-Takagi problem, Math. USSR Sbornik, 15: 31–73 (1971).

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  2. V.M. Adamjan, D.Z. Arov, and M.G. Krein, Infinite block Hankel matrices and related extension problems, American Math. Society Transactions, 111: 133–156 (1978).

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  3. A.C. Antoulas, Approximation of linear operators in the 2-norm, Linear Algebra and its Applications, Special Issue on“Challenges in Linear Algebra”, to appear (1998).

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  4. J. A. Ball, I. Gohberg, and L. Rodman, Interpolation of rational matrix functions, Operator Theory: Advances and Applications, Birkhäuser (1990).

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  5. K. Glover, All optimal Hankel-norm approximations of linear multivariable systems and their L ∞-error bounds, International Journal of Control, 39: 1115–1193 (1984).

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  6. A.J. van der Veen, A Schur method for low rank matrix approximation, SIAM J. Matrix Analysis and Applications, January (1996).

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  7. J.C. Willems, From time series to linear system — Part III: Approximate modeling, Automatica 23: 87–115 (1987).

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Author information

Authors and Affiliations

  1. Department of Electrical Engineering, Rice University, Houston, TX, 77251, USA

    A. C. Antoulas

Authors
  1. A. C. Antoulas
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Editor information

Editors and Affiliations

  1. Institute of Mathematics, University of Leige, Sart Tilman B37, B-4000, Liege, Belgium

    Vincent Blondel (PhD) (PhD)

  2. Department of Mathematics, Rutgers University, Hill Center 724, 08903, New Brunswick, USA

    Eduardo D. Sontag (PhD) (PhD)

  3. Centre for Arificial Intelligence and Robotics, Raj Bhavan Cirlce - High Grounds, 560001, Bangalore, India

    Mathukumalli Vidyasagar (PhD) (PhD)

  4. Institute of Mathematics, Rijksuniversiteit te Groningen, Postbus 800, 9700, Av Groningen, The Netherlands

    Jan C. Willems (PhD) (PhD)

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© 1999 Springer-Verlag London Limited

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Antoulas, A.C. (1999). System approximation in the 2-norm. In: Blondel, V., Sontag, E.D., Vidyasagar, M., Willems, J.C. (eds) Open Problems in Mathematical Systems and Control Theory. Communications and Control Engineering. Springer, London. https://doi.org/10.1007/978-1-4471-0807-8_3

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  • DOI: https://doi.org/10.1007/978-1-4471-0807-8_3

  • Publisher Name: Springer, London

  • Print ISBN: 978-1-4471-1207-5

  • Online ISBN: 978-1-4471-0807-8

  • eBook Packages: Springer Book Archive

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