Nodal performance measures for oscillator networks with local and global damping

This paper proposes and characterizes a pairwise performance measure for two arbitrary nodes in a network of coupled oscillators. The measure is based upon the steady state variance of the difference between the phases of the node pair due to network level disturbances. For two adjacent nodes this quantity corresponds to the total interactions over the edge connecting the nodes. When the two oscillators are not adjacent it is a measure of the coherence of the subnetwork defined by the two nodes. For the special case of two nodes connected by a single path our analytical results show that coherence in this subnetwork is independent of the nodes outside this path in first order networks and second order oscillator networks with global damping. However, computing the performance of oscillator networks with local damping requires the full network. These results allow one to isolate the performance of subsystems of interest or to evaluate the effect of changing the network topology of particular subsystems in, for example, large vehicle platoons, where local and global damping correspond to local and global velocity feedback.