Partial Synchronization in Networks of Nonlinear Systems with Transmission Delay Couplings*

This paper considers synchronization problems in networks of nonlinear systems that are bidirectionally coupled with time-delay in the transmission signal. By applying equitable partitions to the networks, we derive an LMI-based condition for partial synchronization that implies synchronization in a part of systems in the network. We show that regardless of the length of time-delay, partial synchronization emerges for the coupling strength larger than a threshold value when the proposed condition holds. An illustrated example of a numerical simulation is given to show the validity of the result.