Structure preserving model reduction of second-order time-delay systems via approximate Gramians

In this study, a model-order reduction approach based on approximate Gramians for second-order time-delay systems is proposed. By treating the second-order time-delay system as a special case of the integro-differential system, it exhibits a connection with the time-delay Gramians of the corresponding first-order system. After applying the approximate Gramians and balanced truncation procedures, the resulting reduced system is expected to well approximate the original system. Besides, the ε-embedding technique is applied to the case when the damping matrix of the second-order time-delay system is singular. Finally, numerical examples show the good performance in the time domain and the finite frequency range.