Abstract
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.
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