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The real circuit model, such as a partial element equivalent circuit (PEEC), can be represented as a delay differential equation (DDE) of neutral type. The study of asymptotic stability of this kind of systems is of much importance due to the fragility of DDE solvers. Based on a descriptor system approach, new delay-dependent stability results are derived by introducing some free weighting matrices. As an application of the results, the delay-dependent stability problem of a PEEC model is investigated. The comparison of the results with the existing ones is finally given by using the PEEC model and another numerical example.