Synchronization Preserving Model Reduction of Multi-Agent Network Systems by Eigenvalue Assignments

In this paper, structure preserving model reduction problem for multi-agent network systems consisting of diffusively coupled agents is investigated. A new model reduction method based on eigenvalue assignment is derived. Particularly, the spectrum of the reduced textit{Laplacian matrix} is selected as a subset of the spectrum of the original textit{Laplacian matrix}. The resulting reduced-order model retains the network protocol of diffusive couplings, and thus the synchronization property is preserved. Moreover, a concise expression for the upper-bound of the mathcal{H}_{2} approximation error is presented in the setting of a leader-follower network, and it provides a guideline to select the eigenvalues of the reduced textit{Laplacian matrix}. The effectiveness of the proposed method is finally illustrated via the application to a spacecraft network, with a comparison of performances with the graph clustering method in cite{monshizadeh2014projection} and balanced truncation approach in cite{cheng2017balancedb}.