About disconnected topologies and synchronization of homogeneous nonlinear agents over switching networks

In this paper, we study the problem of networks on nonlinear oscillators when communication topologies are disconnected. In the first part of this paper, we show that the high‐gain design procedure succeeds in achieving clustered consensus when disconnected topologies occur. In the second part, we study a network of nonlinear oscillators when the topology is switching between sets of disconnected and connected topologies. By a Lyapunov analysis, we prove that if disconnected topologies last for a limited amount of time and the switching law for connected topologies fulfills an average dwell‐time condition, synchronization is achieved.