Model Order Reduction of Linear Systems via the Cross Gramian and SVD

On the basis of the cross Gramian and the singular value decomposition, this brief investigates model order reduction of linear time-invariant systems in the view of the symmetric case and the nonsymmetric case. It guarantees the reduced system for the nonsymmetric system to be data-sparse. The asymptotical stability of the reduced system is discussed and an output error bound is provided. The correlation of the Hankel singular values in the proposed method and the balanced truncation method is presented. Finally, numerical results indicate that the reduced system of the symmetric system is equivalent to that resulting from balanced truncation, while the reduced system of the nonsymmetric system has a good performance.