Complementary matrices in the inclusion principle for dynamic controllers

Lubomír Bakule; José Rodellar; Josep M. Rossell

Kybernetika (2003)

  • Volume: 39, Issue: 3, page [369]-385
  • ISSN: 0023-5954

Abstract

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A generalized structure of complementary matrices involved in the input-state- output Inclusion Principle for linear time-invariant systems (LTI) including contractibility conditions for static state feedback controllers is well known. In this paper, it is shown how to further extend this structure in a systematic way when considering contractibility of dynamic controllers. Necessary and sufficient conditions for contractibility are proved in terms of both unstructured and block structured complementary matrices for general expansion/contraction transformation matrices. Explicit sufficient conditions for blocks of complementary matrices ensuring contractibility are proved for general expansion/contraction transformation matrices. Moreover, these conditions are further specialized for a particular class of transformation matrices. The results are derived in parallel for two important cases of the Inclusion Principle namely for the case of expandability of controllers and the case of extensions.

How to cite

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Bakule, Lubomír, Rodellar, José, and Rossell, Josep M.. "Complementary matrices in the inclusion principle for dynamic controllers." Kybernetika 39.3 (2003): [369]-385. <http://eudml.org/doc/33651>.

@article{Bakule2003,
abstract = {A generalized structure of complementary matrices involved in the input-state- output Inclusion Principle for linear time-invariant systems (LTI) including contractibility conditions for static state feedback controllers is well known. In this paper, it is shown how to further extend this structure in a systematic way when considering contractibility of dynamic controllers. Necessary and sufficient conditions for contractibility are proved in terms of both unstructured and block structured complementary matrices for general expansion/contraction transformation matrices. Explicit sufficient conditions for blocks of complementary matrices ensuring contractibility are proved for general expansion/contraction transformation matrices. Moreover, these conditions are further specialized for a particular class of transformation matrices. The results are derived in parallel for two important cases of the Inclusion Principle namely for the case of expandability of controllers and the case of extensions.},
author = {Bakule, Lubomír, Rodellar, José, Rossell, Josep M.},
journal = {Kybernetika},
keywords = {linear time-invariant continuous-time systems; dynamic controllers; inclusion principle; large scale systems; overlapping; decomposition; decentralization; linear time-invariant continuous-time systems; dynamic controllers; inclusion principle; large scale systems; overlapping; decomposition; decentralization},
language = {eng},
number = {3},
pages = {[369]-385},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Complementary matrices in the inclusion principle for dynamic controllers},
url = {http://eudml.org/doc/33651},
volume = {39},
year = {2003},
}

TY - JOUR
AU - Bakule, Lubomír
AU - Rodellar, José
AU - Rossell, Josep M.
TI - Complementary matrices in the inclusion principle for dynamic controllers
JO - Kybernetika
PY - 2003
PB - Institute of Information Theory and Automation AS CR
VL - 39
IS - 3
SP - [369]
EP - 385
AB - A generalized structure of complementary matrices involved in the input-state- output Inclusion Principle for linear time-invariant systems (LTI) including contractibility conditions for static state feedback controllers is well known. In this paper, it is shown how to further extend this structure in a systematic way when considering contractibility of dynamic controllers. Necessary and sufficient conditions for contractibility are proved in terms of both unstructured and block structured complementary matrices for general expansion/contraction transformation matrices. Explicit sufficient conditions for blocks of complementary matrices ensuring contractibility are proved for general expansion/contraction transformation matrices. Moreover, these conditions are further specialized for a particular class of transformation matrices. The results are derived in parallel for two important cases of the Inclusion Principle namely for the case of expandability of controllers and the case of extensions.
LA - eng
KW - linear time-invariant continuous-time systems; dynamic controllers; inclusion principle; large scale systems; overlapping; decomposition; decentralization; linear time-invariant continuous-time systems; dynamic controllers; inclusion principle; large scale systems; overlapping; decomposition; decentralization
UR - http://eudml.org/doc/33651
ER -

References

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