  In this paper, we develop a novel unified methodology for performance and
robustness analysis of linear dynamical networks. We introduce the notion of
systemic measures for the class of first--order linear consensus networks. We
classify two important types of performance and robustness measures according
to their functional properties: convex systemic measures and Schur--convex
systemic measures. It is shown that a viable systemic measure should satisfy
several 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 robustness
measures from the literature and show that they all belong to the class of
systemic measures. Moreover, we introduce new classes of systemic measures
based on (a version of) the well--known Riemann zeta function, input--output
system norms, and etc. Then, it is shown that for a given linear dynamical
network one can take several different strategies to optimize a given
performance and robustness systemic measure via convex optimization. Finally,
we characterized an interesting fundamental limit on the best achievable value
of a given systemic measure after adding some certain number of new weighted
edges to the underlying graph of the network.
