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Stabilization of time-delay systems through linear differential equations using a descriptor representation

In this article, a new method to assess stability and to design static state feedback controller for linear time-delay systems is introduced. The method based on linear differential equations allows considering explicit Lyapunov-Krasovskii functionals with non constant matrix parameters. The stability conditions considering constant delays are delay-dependent and expressed using easy computable linear matrix inequalities. An example is introduced to show the efficiency of the stabilization criteria.