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Analysis and Optimization of Systems pp 555–561Cite as

Almost noninteracting control design using dynamic state feedback

  • Algebraic And Geometric System Theory
  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 28))

Abstract

In this paper we will solve, for finite dimensional linear time invariant systems, the problem of the existence of a dynamic state feedback control law such that in the closed loop system the exogenous variables are noninteracting to any arbitrary degree of accuracy. The solvability conditions for this problem involve the recently introduced notion of ‘almost A(mod B)-invariant subspaces’, much in the same way as the completely noninteracting control design involves A(mod B)-invariant subspaces.

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References

  1. W.M. Wonham: Linear Multivariable Control: a Geometric Approach (Second Edition), Springer Verlag, 1979.

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  2. J.C. Willems: "Almost A(mod B)-invariant Subspaces" pp. 239–248 of Analyse des Systèmes, Astérisque, 75–76, 1980.

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  3. J.C. Willems: "Almost Invariant Subspaces: An Approach to High Gain Feedback Design. Part 1: Almost Controlled Invariant Subspaces", to appear in IEEE Trans. Automatic Control, Vol. AC-26, No. 1, 1981.

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  4. J. Descusse: Contribution à la Théorie du Découplage des Quadruplets Linéaires Invariants (A,B,C,D), Thèse de Docteur ès Sciences, Un. de Nantes, Lab. d'Automatique, Ec. Nat. Sup. de Mécanique, 1980.

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  5. M.L.J. Hautus and M. Heymann: "Linear Decoupling: A Transfer Function Analysis", Submitted for publication.

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  6. J.C. Willems and C. Commault: "Disturbance Decoupling by Measurement Feedback with Stability or Pole Placement" to appear in SIAM J. on Control and Optimization.

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Authors and Affiliations

  1. Mathematics Institute, University of Groningen, P.O. Box 800, 9700 AV, Groningen, The Netherlands

    J. C. Willems

Authors
  1. J. C. Willems
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Editor information

A. Bensoussan J. L. Lions

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© 1980 Springer-Veralg

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Willems, J.C. (1980). Almost noninteracting control design using dynamic state feedback. In: Bensoussan, A., Lions, J.L. (eds) Analysis and Optimization of Systems. Lecture Notes in Control and Information Sciences, vol 28. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0004066

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  • DOI: https://doi.org/10.1007/BFb0004066

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-10472-8

  • Online ISBN: 978-3-540-38489-2

  • eBook Packages: Springer Book Archive

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