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Synchronisation of systems with individual dynamics by static networked controllers

The paper deals with the synchronisation of subsystems that have individual linear dynamics. To formulate the basic condition under which the subsystems can be synchronised, the notion of system intersection is introduced. Subsystems can be synchronised by an appropriate controller only if their dynamics have a non‐empty intersection, which acts as a virtual reference system. The paper describes an algorithm for determining the maximum intersection of linear systems and gives an explicit relation for the initial state in dependence upon the subsystem initial states, for which the virtual reference system generates the synchronous trajectory.