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.