mathcal{H}_{2} Sub-Optimal Model Reduction for Second-Order Network Systems (I)

This paper studies a moment matching model reduction method for second-order network systems. For a given complex second-order network system, our goal is to find a reduced second-order network system that achieves moment matching. Firstly, the original second-order network system is split into an asymptotically stable subsystem and an average subsystem. Then, moment matching approach is implemented to reduce the dimension of the asymptotically stable subsystem. The resulting reduced-order model is combined with the average subsystem, leading to a reduced second-order system preserves the semistability. Subsequently, a specific coordinate transform allows for the reduced-order model to be converted to a complete network. A mass-spring-damper network demonstrates the effectiveness of the proposed method.