A New result on stability analysis and H ∞ dynamic output feedback controller for systems with time-varying delays

El khaloufi Ghizlane; Chaibi Noreddine; Boumhidi Ismail; El jimi Driss

Kybernetika (2025)

  • Issue: 2, page 202-220
  • ISSN: 0023-5954

Abstract

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The stability and stabilization of systems with time-varying delays and external disturbances are the subject of this study. To circumvent the limitation of the Bessel-Legendre inequality, which cannot treat a time-varying delay system because the resulting limit contains reciprocal convexity, the generalized free-matrix-based integral inequality is used to generate less conservative stability criteria. Improved stabilization requirements are proposed in the form of linear matrix inequalities by developing a new augmented Lyapuno-Krasovskii function. To achieve resolved controller gains, a method for designing a H ∞ dynamic output feedback controller based on linear matrix inequalities is then provided. Finally, three examples are used to validate the advantages of the approach over existing methods.

How to cite

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Ghizlane, El khaloufi, et al. "A New result on stability analysis and $H_{\infty }$ dynamic output feedback controller for systems with time-varying delays." Kybernetika (2025): 202-220. <http://eudml.org/doc/299983>.

@article{Ghizlane2025,
abstract = {The stability and stabilization of systems with time-varying delays and external disturbances are the subject of this study. To circumvent the limitation of the Bessel-Legendre inequality, which cannot treat a time-varying delay system because the resulting limit contains reciprocal convexity, the generalized free-matrix-based integral inequality is used to generate less conservative stability criteria. Improved stabilization requirements are proposed in the form of linear matrix inequalities by developing a new augmented Lyapuno-Krasovskii function. To achieve resolved controller gains, a method for designing a $H_\infty $ dynamic output feedback controller based on linear matrix inequalities is then provided. Finally, three examples are used to validate the advantages of the approach over existing methods.},
author = {Ghizlane, El khaloufi, Noreddine, Chaibi, Ismail, Boumhidi, Driss, El jimi},
journal = {Kybernetika},
keywords = {stability; stabilization; free-matrix-based integral inequality; linear matrix inequality; $H_\{\infty \}$ dynamic output feedback controller},
language = {eng},
number = {2},
pages = {202-220},
publisher = {Institute of Information Theory and Automation AS CR},
title = {A New result on stability analysis and $H_\{\infty \}$ dynamic output feedback controller for systems with time-varying delays},
url = {http://eudml.org/doc/299983},
year = {2025},
}

TY - JOUR
AU - Ghizlane, El khaloufi
AU - Noreddine, Chaibi
AU - Ismail, Boumhidi
AU - Driss, El jimi
TI - A New result on stability analysis and $H_{\infty }$ dynamic output feedback controller for systems with time-varying delays
JO - Kybernetika
PY - 2025
PB - Institute of Information Theory and Automation AS CR
IS - 2
SP - 202
EP - 220
AB - The stability and stabilization of systems with time-varying delays and external disturbances are the subject of this study. To circumvent the limitation of the Bessel-Legendre inequality, which cannot treat a time-varying delay system because the resulting limit contains reciprocal convexity, the generalized free-matrix-based integral inequality is used to generate less conservative stability criteria. Improved stabilization requirements are proposed in the form of linear matrix inequalities by developing a new augmented Lyapuno-Krasovskii function. To achieve resolved controller gains, a method for designing a $H_\infty $ dynamic output feedback controller based on linear matrix inequalities is then provided. Finally, three examples are used to validate the advantages of the approach over existing methods.
LA - eng
KW - stability; stabilization; free-matrix-based integral inequality; linear matrix inequality; $H_{\infty }$ dynamic output feedback controller
UR - http://eudml.org/doc/299983
ER -

References

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