Practical Synchronization of Perturbed Networks of Semi-Passive Systems

We study practical synchronization for heterogeneous networks of nonlinear systems in the presence of bounded perturbations. Under the assumption that the nodes are state semi-passive and the interconnection graph admits a spanning tree, we establish uniform ultimate boundedness of the solutions and, consequently, practical synchronization. That is, we show that the systems’ trajectories approach each other up to a steady-state error. The magnitude of this steady-state error can be made arbitrarily small by increasing a scalar coupling gain. The results are shown to hold under the assumption that (at least) a single “well-located” node in the network enjoys some robustness properties. Our theoretical results are fairly general in regards to the topology and are illustrated in simulation on a case-study of networked mobile robots.