Bipartite Synchronization of Coupled Linear Homogeneous Systems Subjected to Input Saturation

In this paper, bipartite synchronization is investigated for coupled linear homogeneous systems subjected to input saturation. The problem is pertinent to the underlying signed directed graph (digraph) where both cooperation and competition exist between the systems. A state feedback low-gain controller parameterized in a small positive scalar is constructed based on suitably chosen scalar coupling gain and feedback gain matrix to realize the control problem. Bipartite synchronization phenomenon with respect to a leader system is achieved with the designed control law over the underlying signed digraph network where the digraph contains a directed spanning tree rooted at the leader. Finally, the theoretical results are validated using a group of coupled Chua's circuits which establish the effectiveness of the proposed method.