Scalable Coherence in Large Scale Second-Order Networks Using High-Gain Observer

We propose a scalable second-order consensus algorithm where by tuning the controller parameter, the convergence rate of the consensus protocol is almost invariant with respect to the size of the network. This is beneficial when the algebraic connectivity of the graph Laplacian decreases towards zero, with an increase in the network size, which leads to degraded closed-loop performance. We realize the controller using a high-gain observer and it is shown that for sufficiently small observer parameter, the convergence rate under output feedback approaches the one under state feedback. We also study the controller performance under stochastic disturbances by first defining a performance output and then calculating the ℋ 2 norm from the disturbance input to the performance output. We show that the ℋ 2 norm for the state feedback controller is scalable as the network size increases. Moreover, we also show that for sufficiently small observer parameter, the ℋ 2 norm under output feedback approaches the one under state feedback.