Bipartite synchronization of Lur'e network under signed digraph

This paper considers the bipartite leaderless and leader-following synchronization in a network of coupled Lur'e systems with sector-condition node dynamics and signed digraph topology, where the interaction digraph consists of both positive and negative communication links. Continuous-time and sampled-data control algorithms are, respectively, proposed to solve the bipartite synchronization problems for the signed Lur'e network. Under some assumptions on the network structure and node functions, some bipartite synchronization conditions are established for signed Lur'e network by using coordinate transform, linear matrix inequalities, and algebraic graph theories. For the continuous-time control algorithms, it is shown that the bipartite synchronization problems of the signed Lur'e network can always be solved if the coupling strength is sufficiently large and the network topology satisfies some suitable conditions. For the sampled-data control algorithms, an upper bound of the sampling intervals is estimated to ensure that the bipartite synchronization can be reached in the signed Lur'e network. Some simulation results are given to illustrate the effectiveness of the theoretical analysis.