Consensus of nonlinear second-order multi-agent systems with mixed time-delays and intermittent communications

The paper investigates second-order consensus problem of nonlinear multi-agent systems with mixed time-delays and intermittent communications, where the mixed time-delays are composed of discrete and distributed delays, and each agent is assumed to obtain the relatively completely intermittent information of neighboring agents due to communication constraints. A new kind of distributed control protocol is designed based on the adaptive intermittent control ideas, some novel criteria are derived in matrix inequalities form by resorting to the generalized Halanay inequality. It is proved that second-order consensus can be reached if communication duration is larger than a threshold value under the strongly connected and balanced topology, and the relationship between the delays and communication duration over each control period is sought out. Finally, two simulation examples are provided to illustrate the effectiveness of the obtained theoretical results.