On some relaxations commonly used in the study of linear systems

Olivier Bachelier; Driss Mehdi

Kybernetika (2015)

  • Volume: 51, Issue: 5, page 830-855
  • ISSN: 0023-5954

Abstract

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This note proposes a quite general mathematical proposition which can be a starting point to prove many well-known results encountered while studying the theory of linear systems through matrix inequalities, including the S-procedure, the projection lemma and few others. Moreover, the problem of robustness with respect to several parameter uncertainties is revisited owing to this new theorem, leading to LMI (Linear Matrix Inequality)-based conditions for robust stability or performance analysis with respect to ILFR (Implicit Linear Fractional Representation)-based parametric uncertainty. These conditions, though conservative, are computationally very tractable and make a good compromise between conservatism and engineering applicability.

How to cite

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Bachelier, Olivier, and Mehdi, Driss. "On some relaxations commonly used in the study of linear systems." Kybernetika 51.5 (2015): 830-855. <http://eudml.org/doc/276175>.

@article{Bachelier2015,
abstract = {This note proposes a quite general mathematical proposition which can be a starting point to prove many well-known results encountered while studying the theory of linear systems through matrix inequalities, including the S-procedure, the projection lemma and few others. Moreover, the problem of robustness with respect to several parameter uncertainties is revisited owing to this new theorem, leading to LMI (Linear Matrix Inequality)-based conditions for robust stability or performance analysis with respect to ILFR (Implicit Linear Fractional Representation)-based parametric uncertainty. These conditions, though conservative, are computationally very tractable and make a good compromise between conservatism and engineering applicability.},
author = {Bachelier, Olivier, Mehdi, Driss},
journal = {Kybernetika},
keywords = {LMI relaxations; robust analysis; parametric uncertainty},
language = {eng},
number = {5},
pages = {830-855},
publisher = {Institute of Information Theory and Automation AS CR},
title = {On some relaxations commonly used in the study of linear systems},
url = {http://eudml.org/doc/276175},
volume = {51},
year = {2015},
}

TY - JOUR
AU - Bachelier, Olivier
AU - Mehdi, Driss
TI - On some relaxations commonly used in the study of linear systems
JO - Kybernetika
PY - 2015
PB - Institute of Information Theory and Automation AS CR
VL - 51
IS - 5
SP - 830
EP - 855
AB - This note proposes a quite general mathematical proposition which can be a starting point to prove many well-known results encountered while studying the theory of linear systems through matrix inequalities, including the S-procedure, the projection lemma and few others. Moreover, the problem of robustness with respect to several parameter uncertainties is revisited owing to this new theorem, leading to LMI (Linear Matrix Inequality)-based conditions for robust stability or performance analysis with respect to ILFR (Implicit Linear Fractional Representation)-based parametric uncertainty. These conditions, though conservative, are computationally very tractable and make a good compromise between conservatism and engineering applicability.
LA - eng
KW - LMI relaxations; robust analysis; parametric uncertainty
UR - http://eudml.org/doc/276175
ER -

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