Performance analysis of linear consensus networks with structured stochastic disturbance inputs

In this paper, we investigate global performance deterioration of linear consensus networks subject to exogenous disturbance inputs. It is assumed that the dynamics of the network is influenced by two types of external disturbances: additive noise input and measurement noise. The effect of these disturbance inputs on the global performance of the network is measured by the square of the ℋ₂-norm of the system from the disturbance inputs to the outputs. We exploit the structure of the underlying graph of the network in order to derive explicit expressions for the performance measure in terms of the underlying graph structure. Finally, we consider several scenarios and characterize several scaling laws for each case and show that the performance measure scales with the network size.