Bipartite Consensus for Multi-Agent Systems With Time-Varying Delays Based on Method of Delay Partitioning

Bipartite consensus protocol is designed for multi-agent systems with time-varying delays. Then, the bipartite consensus problem is transformed into a corresponding stability problem by methods of gauge transformation and state transformation. The Lyapunov-Krasovskii functional is constructed, and the linear matrix inequality theory based on methods of delay partitioning and free matrix integral inequality is used to obtain sufficient conditions for a bipartite consensus of multi-agent systems. Both the first-order and second-order multi-agent systems are investigated. Finally, the effectiveness of the obtained results is illustrated by virtue of simulation results.