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


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’.


Structural Feature System Theory Feedback Loop Mathematical Method System Parameter 
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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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