H2 Analysis and Synthesis of Networked Dynamic Systems

This work provides a general framework for the analysis and synthesis of a class of linear networked dynamic systems (NDS). We focus our attention on NDS where the underlying connection topology couples the agents at their outputs. A distinction is made between NDS with homogeneous agent dynamics and NDS with heterogeneous agent dynamics. In the homogeneous setting, the H2 norm expression reduces to the Frobenius norm of the underlying connection topology incidence matrix, E(G), scaled by the H2 norm of the agents comprising the NDS. In the heterogeneous case, the H2 norm becomes the weighted Frobenius norm of the incidence matrix, where the weights appear on the nodes of the graph. The H2 norm characterization is then used to synthesize NDS with certain H2 performance. Specifically, a semi-definite programming solution is presented to design a local controller for each agent when the underlying topology is fixed. A solution using Kruskal’s algorithm for finding a minimum weight spanning tree is used to design the optimal NDS topology given fixed agent dynamics.