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Keywords:
stability; stabilization; free-matrix-based integral inequality; linear matrix inequality; $H_{\infty }$ dynamic output feedback controller
stability; stabilization; free-matrix-based integral inequality; linear matrix inequality; $H_{\infty }$ dynamic output feedback controller
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.
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