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

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.