Special structural Gramian approximation methods for model order reduction of time-delay systems

Model order reduction methods via low-rank approximation of Gramians for time-delay systems are developed in this paper. The main contribution is to achieve the balancing and truncation of the system by utilizing low-rank decomposition of the Gramians combined with the low-rank square root framework. Here, based on Laguerre expansion technique, the low-rank factorization of the system Gramians is realized via a linear system with special structure, thus enabling an efficient implementation of the reduction process. Furthermore, the issue of stability preservation is briefly described. We employ the dominant subspaces projection model reduction method to mitigate the effects which may accidentally produce unstable reduced models. Finally, numerical results verify the performance of the approximation-Gramian methods.