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A New result on stability analysis and $H_{\infty }$ dynamic output feedback controller for systems with time-varying delays

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Title: A New result on stability analysis and $H_{\infty }$ dynamic output feedback controller for systems with time-varying delays
Authors: Ghizlane, El khaloufi, Noreddine, Chaibi, Ismail, Boumhidi, Driss, El jimi
Publisher Information: Institute of Information Theory and Automation AS CR
Publication Year: 2025
Collection: DML-CZ (Czech Digital Mathematics Library)
Subject Terms: keyword:stability, keyword:stabilization, keyword:free-matrix-based integral inequality, keyword:linear matrix inequality, keyword:$H_{\infty }$ dynamic output feedback controller, msc:93B52, msc:93Dxx
Description: summary: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.
Document Type: text
File Description: application/pdf
Language: English
ISSN: 0023-5954
1805-949X
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Availability: http://hdl.handle.net/10338.dmlcz/152988
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Accession Number: edsbas.8929325E
Database: BASE
Description
Abstract:summary: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.
ISSN:00235954
1805949X