Output Synchronization of Nonlinear Systems with Time Delay in Communication

In this paper we consider the problem of output synchronization in multi-agent systems where the coupling among the agents is nonlinear and there are time delays in communication. We assume that dynamics of each agent are passive with a positive definite storage function. In the delay free case, the output synchronization results for nonlinear coupling closely follow our earlier results with linear coupling. We show that if the agents are coupled using passive nonlinear controls, namely a class of sector nonlinearities, the agents output synchronizes. In the case of linear coupling among the agents, we have shown previously that the outputs synchronize for various communication topologies even with time delay in communication. The case of nonlinear coupling with delay is more difficult. In this paper we show that output synchronization is achievable with modified communication architecture. Instead of sending the output of each agent across the communication channel, we first encode the output information using the scattering variables, and we transmit the scattering variables across the network. The scattering variable formulation pacifies the communication channel and allows output synchronization independent of the (constant) communication delay