Time-delay system approach to delay independent stability analysis and controller synthesis

In this paper, we address the delay independent stability analysis and control of time-delay systems with parameter-dependent, possibly time-varying, uncertainties. Firstly, we see the Lyapunov-Krasovskii´s method and the Razumikhin´s method are approach to time-invariant time-delay independent stability. Then we present an extension of this condition to time-varying parameter-dependent time-delay systems. Using parameter-dependent Lyapunov function and employing free-weighting matrices, this extension states robust admissibility linear matrix inequality (LMI) conditions that are less restrictive, as demonstrated by numerical examples, than the existing one. In order to solving state-feedback controller, we also present in this paper a new robust admissibility analysis result, which directly obtain the state-feedback controller.