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In this paper, we develop a novel unified methodology for performance androbustness analysis of linear dynamical networks. We introduce the notion ofsystemic measures for the class of first--order linear consensus networks. Weclassify two important types of performance and robustness measures accordingto their functional properties: convex systemic measures and Schur--convexsystemic measures. It is shown that a viable systemic measure should satisfyseveral fundamental properties such as homogeneity, monotonicity, convexity,and orthogonal invariance. In order to support our proposed unified framework,we verify functional properties of several existing performance and robustnessmeasures from the literature and show that they all belong to the class ofsystemic measures. Moreover, we introduce new classes of systemic measuresbased on (a version of) the well--known Riemann zeta function, input--outputsystem norms, and etc. Then, it is shown that for a given linear dynamicalnetwork one can take several different strategies to optimize a givenperformance and robustness systemic measure via convex optimization. Finally,we characterized an interesting fundamental limit on the best achievable valueof a given systemic measure after adding some certain number of new weightededges to the underlying graph of the network.

Systemic Measures for Performance and Robustness of Large-Scale Interconnected Dynamical Networks