Robust synchronisation of unstable linear time-invariant systems

A framework based on the gap metric and integral quadratic constraints (IQCs) is developed for analysing robust synchronisation of heterogenous linear time-invariant networks. Both the agents and the communication channels are allowed to be dynamic and unstable. Structural properties of the uncertainty are described by IQCs and exploited in synchronisation analysis as a means to reduce conservatism. The homotopy employed in IQC analysis is defined with respect to the graph topology as induced by the gap metric, whereby open-loop unstable dynamics are accommodated. The results in this paper extend recent developments, which have been shown to unify several existing synchronisation analysis methods in the literature.