Stability of networked systems: A multi-scale approach using contraction

This paper is concerned with the stability of networked control systems. Using contraction theory, a result is established on the network structure and the properties of the individual component subsystems and their couplings to ensure the overall contractivity of the entire network. Specifically, it is shown that a contraction property on a reduced-order matrix that quantifies the interconnection structure, coupled with contractivity/expansion estimates on the individual component subsystems, suffices to ensure that nearby trajectories of the overall system converge towards each other. The paper also describes a relative contraction result of interest in synchronization problems.