Non-Trivial Output Synchronization of Heterogeneous Passive Systems

In this technical note, we present conditions for non-trivial output synchronization in heterogeneous networks of passive linear systems. A network is said to be non-trivially output synchronized if its individual system outputs asymptotically converge to a common trajectory that is not identically zero. Though conditions for output synchronization in a heterogeneous network of passive systems have been revealed in previous literature, those conditions do not provide a criterion to check whether the network is synchronized trivially or non-trivially. Furthermore, we hardly found simulation results in the literature showing the non-trivial synchronization. In this technical note, we present necessary and sufficient conditions for the non-trivial output synchronization based on properties of passive linear systems and internal model principle. In addition, we present a systematic procedure for the realization of the internal model which fully satisfies the presented conditions.