On output consensus of heterogeneous dynamical networks

TL;DR

This paper studies how interconnected heterogeneous dynamical networks can achieve output consensus despite differences among subsystems, by introducing an index measuring heterogeneity and establishing conditions based on network connectivity.

Contribution

It introduces a novel heterogeneity index and provides conditions linking heterogeneity and connectivity to output consensus in heterogeneous networks.

Findings

Heterogeneity index quantifies differences between subsystems.

Connectivity conditions ensure output consensus.

Framework applies to networks with external disturbances.

Abstract

This work is concerned with interconnected networks with non-identical subsystems. We investigate the output consensus of the network where the dynamics are subject to external disturbance and/or reference input. For a network of output-feedback passive subsystems, we first introduce an index that characterises the gap between a pair of adjacent subsystems by the difference of their input-output trajectories. The set of these indices quantifies the level of heterogeneity of the networks. We then provide a condition in terms of the level of heterogeneity and the connectivity of the networks for ensuring the output consensus of the interconnected network.