Robust Synchronization in Multi-Agent Networks With Unstable Dynamics

The problem of synchronization in heterogenous linear time-invariant networks is investigated. An approach blending the theory of integral quadratic constraints (IQCs) with the gap metric is proposed to study the problem within a unifying framework, where both the agents and communication channels can be dynamic, infinite-dimensional, unstable, and uncertain. Structural properties of the uncertainty are described by IQCs and exploited in the analysis to reduce conservatism. The homotopy employed in IQC analysis is defined with respect to the graph topology induced by the gap metric, whereby open-loop unstable dynamics are accommodated. Sufficient conditions for synchronism are provided, extending recent developments which have been shown to unify several existing synchronization analysis results in the literature.