Model Order Reduction Based on Approximate Cross Gramian and Laguerre Series for Linear Input-Output Systems

In this paper, we first focus on the topic of calculation of cross gramians for linear square systems, which are constructed approximately from the Laguerre series expansion coefficient vectors that are obtained by solving a recurrence formula instead of solving Sylvester equations directly. Then based on such approximate cross gramian, the reduced-order models (ROMs) are produced by truncating the states that are associated with the smaller approximate Hankel singular values (HSVs). In addition, combining with the idea of dominant subspace projection method, we modify our proposed algorithm to obtain a ROM that preserves the stability. What's more, our algorithms are extended to non-square case successfully. The main properties of ROMs are discussed as well. Finally, some numerical simulations are provided to illustrate the effectiveness of our proposed algorithms in the views of accuracy and computational cost.