针对具有时变时滞的多智能体系统二分一致性问题, 设计出相应的一 致性协议. 进一步, 通过规范变换和状态变换将二分一致性问题转化为相应的稳 定性问题. 构造Lyapunov-Krasovskii泛函, 利用线性矩阵不等式(LMI)理论并结合自由矩阵的方法得到多智能体系统达到二分一致的充分条件. 对于固定拓扑和切换拓扑情形均进行了研究, 当系统具有切换拓扑时, 利用平均驻留时间方法分析得到保证系统二分一致性成立的充分条件. 最后, 利用仿真实例说明所得结果的有效性.

Consensus protocol is designed for bipartite consensus of multi-agent systems with time-varying delays. Further, the bipartite consensus problem is transformed into a stability problem by a gauge transformation and a state transformation. Lyapunov-Krasovskii functional is constructed and the linear matrix inequality (LMI) theory and the method of free matrix are used to obtain the sufficient conditions for bipartite consensus of multi-agent systems. The cases of fixed topology and switching topologies are both investigated and the method of average dwell time is used to get sufficient conditions to guarantee bipartite consensus when the systems have switching topologies. Finally, the effectiveness of the obtained results is illustrated by virtue of simulation results.