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Applied Mathematics and Optimization

, Volume 2, Issue 2, pp 170–194 | Cite as

The internal model principle for linear multivariable regulators

  • B. A. Francis
  • W. M. Wonham
Article

Abstract

Necessary structural criteria are obtained for linear multivariable regulators which retain loop stability and output regulation in the presence of small perturbations, of specified types, in system parameters. It is shown that structural stability thus defined requires feedback of the regulated variable, together with a suitably reduplicated model, internal to the feedback loop, of the dynamic structure of the exogenous reference and disturbance signals which the regulator is required to process. Necessity of these structural features constitutes the ‘internal model principle’.

Keywords

Structural Feature System Theory Feedback Loop Mathematical Method System Parameter 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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    W. M. Wonham,Linear Multivariable Control: A Geometric Approach, Lecture Notes in Economics and Mathematical Systems, Vol. 101, Springer-Verlag, New York, 1974.Google Scholar
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    F. R. Gantmacher,The Theory of Matrices, Vol. 1, Chelsea, New York, 1959.Google Scholar
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    B. A. Francis andW. M. Wonham, The rôle of transmission zeros in linear multivariable regulators, Control Systems Rpt. No. 7501, Dept. of Electrical Engineering, University of Toronto, February 1975.Google Scholar
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Copyright information

© Springer-Verlag New York Inc. 1975

Authors and Affiliations

  • B. A. Francis
  • W. M. Wonham
    • 1
  1. 1.Department of Electrical EngineeringUniversity of TorontoTorontoCanada

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