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H∞ — Optimal Control, LQG Polynomial Systems Techniques and Numerical Solution Procedures

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Modelling, Robustness and Sensitivity Reduction in Control Systems

Part of the book series: NATO ASI Series ((NATO ASI F,volume 34))

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Abstract

The introductory material first relates the general background of the robustness problem. This is followed by more specific material giving the context for the LQG and polynomial systems approach to the problem of H∞ optimal control design.

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Abbreviations

ℝ:

set of real numbers

ℝn :

n-tuple of real numbers

ℝnxm :

nxm — tuple of real numbers

ℙ(.):

set of polynomials with real coefficients

ℝ(.):

set of ratios a(.)/b(.) where a,b ε ℙ(.)

Toep(A):

Toeplitz matrix formed from A ε ℙ (.)

Toep(A) Δ:

where A = a0 + a1z-1 +...+ anz-n ε ℙ(z-1) and dimensions α, β depend on the order of the polynomial multiplication being represented.

References

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Author information

Authors and Affiliations

  1. Institute of Information Sciences and Electronics, University of Tsukuba, Niiharigun, Ibaraki, 305, Japan

    M. Saeki

  2. Industrial Control Unit, University of Strathclyde, Glasgow, G1 1XW, Scotland, UK

    M. J. Grimble & M. A. Johnson

  3. Department of Applied Mathematics, Twente University of Technology, 7500 AE, Enschede, The Netherlands

    E. Kornegoor

Authors
  1. M. Saeki
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  2. M. J. Grimble
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  3. E. Kornegoor
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  4. M. A. Johnson
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Editor information

Editors and Affiliations

  1. Mathematics Institute, University of Groningen, 9700 AV, Groningen, The Netherlands

    Ruth F. Curtain

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© 1987 Springer-Verlag Berlin Heidelberg

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Saeki, M., Grimble, M.J., Kornegoor, E., Johnson, M.A. (1987). H∞ — Optimal Control, LQG Polynomial Systems Techniques and Numerical Solution Procedures. In: Curtain, R.F. (eds) Modelling, Robustness and Sensitivity Reduction in Control Systems. NATO ASI Series, vol 34. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-87516-8_21

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  • DOI: https://doi.org/10.1007/978-3-642-87516-8_21

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-87518-2

  • Online ISBN: 978-3-642-87516-8

  • eBook Packages: Springer Book Archive

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