Balanced Truncation Approach to Linear Network System Model Order Reduction

In this paper, we propose a model reduction method for semistable Laplacian dynamics, which describe the behaviors of network systems. In the method, the original semistable system is split into an average system and asymptotically stable part. We only implement the balanced truncation to reduce the dimension of the stable part and obtain the reduced-order model preserving the semistability. Then, a specific coordinate transform enables to convert the resulting reduced-order model to the lower-dimensional network system that represents a simplified complete network with less vertices. The reduction procedure allows for the a priori computation of a bound on the approximation error between the original and reduced Laplacian dynamics. Finally, the proposed method is illustrated by an example.