Graph weight design for Laplacian eigenvalue constraints with multi-agent systems applications

We adjust the node and edge weightings of graphs using convex optimization to impose bounds on their Laplacian spectra. We first derive necessary and sufficient conditions that characterize the feasibility of spectral bounds given positive node and edge weightings. Next, we propose algorithms that exploit convexity to achieve these bounds. The design and analysis tools are useful for a variety of stability and control problems in multi-agent systems.