Disturbance Sensitivity Analysis of Evolving Network Systems from Viewpoint of Network Structure

Abstract

This paper performs the disturbance sensitivity analysis of homogeneous network systems, where identical clusters of nodes are interconnected. In particular, each node is described by a dynamical system with a single integrator, which can express a general system including, e.g., a single integrator and a second-order oscillator in first- and second-order consensus network systems. In this analysis, we give attention to external and internal network structures: the network structure among clusters and the network structure among nodes inside each cluster. The main contributions of this paper are twofold. First, we numerically find that, as the number of nodes increases, the disturbance sensitivity of the overall network system, in which disturbance input and evaluation output are assigned at interconnection links among clusters, tends to be reduced if the external network structure is sparse and the internal network structure is dense. Next, to support this finding, we theoretically prove that, in the limit of sufficiently large number of nodes, the minimum disturbance sensitivity level, evaluated by the maximum eigenvalue associated with the external network, is achieved if the internal network structure is given by the complete graph.