Improved results on stability for time-delay descriptor systems

We address the intricate issue of delay-dependent admissibility in descriptor time-delay systems. By employing the powerful generalised integral inequality method and introducing some slack variables, we present a suitable Lyapunov-Krasovskii functional to formulate novel delay-dependent criteria. These criteria not only guarantee the system's regularity and absence of impulses but also establish its stability, all achieved through the utilisation of linear matrix inequalities. To validate the effectiveness of the derived results and facilitate comparison with prior investigations, a numerical example is presented. Through this example, we illustrate the effectiveness and superiority of our proposed criteria over existing studies.