Structure-preserving model order reduction by general orthogonal polynomials for integral-differential systems

For the model order reduction (MOR) of large integral-differential system, how to preserve the featured structure of original system is critical. In this paper, an orthogonal polynomials-based MOR method in time domain for the integral-differential system is presented, which is effective for preserving the structure of the original system. This method directly approximates the time response of the original system. The method is presented via an equivalent state-space system, resulting in an integral-differential reduced system. The stability of the resultant reduced system can be guaranteed under certain conditions. The error between the original system and the reduced system can be estimated. Three benchmarks in practical applications are assessed by employing different MOR methods. Compared to the moment matching method and approximate balancing truncation method, the proposed method possesses superior performance.