In this paper, the H∞ global asymptotic consensus problem with an unweighted \({\mathcal{L}_2}\) gain for the multi-agent switching systems (MASs) with time-varying delays is studied, and utilizing the rigorous mode dependence adaptive double event-triggered scheme (MDADETS) to further save more communication resources. The novel MDADETS is proposed, which can dynamically adjust the event triggering frequency according to the control requirements of the agent, thus can further reduce the status signals reaching the actuator. At the same time, the multiple discrete Lyapunov-Krasovskii functional (LKF) with time-varying matrices is used to reduce the uncertainty brought to the agent at the switching instant, making the increment of LKF less than 1 at the switching instant, thereby reducing the conservatism of MASs. Then, it is proved that the Zeno phenomenon with MDADETS will not occur, which ensures the effectiveness of the novel scheme. Then based on linear matrix inequalities (LMIs) we can deduce the sufficient conditions for H∞ global asymptotic consensus, and obtain parameters such as controller gain and trigger matrix. Finally, numerical simulation is used to verify the operability and superiority of the novel scheme, as well as the effectiveness of the discrete LKF method used in this problem.
