Kybernetika 61 no. 2, 202-220, 2025

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

El khaloufi Ghizlane, Chaibi Noreddine, Boumhidi Ismail and El jimi DrissDOI: 10.14736/kyb-2025-2-0202

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.

Keywords:

stability, linear matrix inequality, stabilization, free-matrix-based integral inequality, $H_{\infty }$ dynamic output feedback controller

Classification:

93Dxx, 93B52

paper.pdf

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