Stability analysis and synthesis of systems subject to norm bounded, bounded rate uncertainties

Francesco Amato

Kybernetika (2000)

  • Volume: 36, Issue: 1, page [21]-29
  • ISSN: 0023-5954

Abstract

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In this paper we consider a linear system subject to norm bounded, bounded rate time-varying uncertainties. Necessary and sufficient conditions for quadratic stability and stabilizability of such class of uncertain systems are well known in the literature. Quadratic stability guarantees exponential stability in presence of arbitrary time-varying uncertainties; therefore it becomes a conservative approach when, as it is the case considered in this paper, the uncertainties are slowly-varying in time. The first contribution of this paper is a sufficient condition for the exponential stability of the zero input system; such condition, which takes into account the bound on the rate of variation of the uncertainties, results to be a less conservative analysis tool than the quadratic stability approach. Then the analysis result is used to provide an algorithm for the synthesis of a controller guaranteeing closed loop stability of the uncertain forced system.

How to cite

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Amato, Francesco. "Stability analysis and synthesis of systems subject to norm bounded, bounded rate uncertainties." Kybernetika 36.1 (2000): [21]-29. <http://eudml.org/doc/33466>.

@article{Amato2000,
abstract = {In this paper we consider a linear system subject to norm bounded, bounded rate time-varying uncertainties. Necessary and sufficient conditions for quadratic stability and stabilizability of such class of uncertain systems are well known in the literature. Quadratic stability guarantees exponential stability in presence of arbitrary time-varying uncertainties; therefore it becomes a conservative approach when, as it is the case considered in this paper, the uncertainties are slowly-varying in time. The first contribution of this paper is a sufficient condition for the exponential stability of the zero input system; such condition, which takes into account the bound on the rate of variation of the uncertainties, results to be a less conservative analysis tool than the quadratic stability approach. Then the analysis result is used to provide an algorithm for the synthesis of a controller guaranteeing closed loop stability of the uncertain forced system.},
author = {Amato, Francesco},
journal = {Kybernetika},
keywords = {quadratic stability of uncertain systems; zero input system; quadratic stability of uncertain systems; zero input system},
language = {eng},
number = {1},
pages = {[21]-29},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Stability analysis and synthesis of systems subject to norm bounded, bounded rate uncertainties},
url = {http://eudml.org/doc/33466},
volume = {36},
year = {2000},
}

TY - JOUR
AU - Amato, Francesco
TI - Stability analysis and synthesis of systems subject to norm bounded, bounded rate uncertainties
JO - Kybernetika
PY - 2000
PB - Institute of Information Theory and Automation AS CR
VL - 36
IS - 1
SP - [21]
EP - 29
AB - In this paper we consider a linear system subject to norm bounded, bounded rate time-varying uncertainties. Necessary and sufficient conditions for quadratic stability and stabilizability of such class of uncertain systems are well known in the literature. Quadratic stability guarantees exponential stability in presence of arbitrary time-varying uncertainties; therefore it becomes a conservative approach when, as it is the case considered in this paper, the uncertainties are slowly-varying in time. The first contribution of this paper is a sufficient condition for the exponential stability of the zero input system; such condition, which takes into account the bound on the rate of variation of the uncertainties, results to be a less conservative analysis tool than the quadratic stability approach. Then the analysis result is used to provide an algorithm for the synthesis of a controller guaranteeing closed loop stability of the uncertain forced system.
LA - eng
KW - quadratic stability of uncertain systems; zero input system; quadratic stability of uncertain systems; zero input system
UR - http://eudml.org/doc/33466
ER -

References

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  7. Geromel J. C., Peres P. L. D., Bernussou J., 10.1137/0329021, SIAM J. Control Optim. 29 (1991), 381–402 (1991) Zbl0741.93020MR1092734DOI10.1137/0329021
  8. Hinrichsen D., Pritchard A. J., 10.1016/0167-6911(86)90094-0, Systems Control Lett. 7 (1986), 1–10 (1986) Zbl0631.93064MR0833059DOI10.1016/0167-6911(86)90094-0
  9. Narendra K. S., Taylor J. H., Frequency Domain Criteria for Absolute Stability, Academic Press, New York 1973 Zbl0266.93037MR0329710
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