Aimed at the problem of actuator failure and network attack, the co-design problem of fault-tolerance and attack-tolerance of NCS was studied under DETCS. Firstly, the framework of NCS with fault-tolerant and attack-tolerant ability was given out under DETCS and based on it, a closed-loop NCS model with coexistent failure and attack was established, which integrated the trigger condition, actuator failure, and network attack into one uniform framework. Secondly, by means of constructing Lyapunov-Krasovskii functional and utilizing comprehensively the time-delay system theory, improved Wirtinger's inequality and reciprocal convex combination lemma, a completeness sufficient condition for fault-tolerant and attack-tolerant NCS was deduced, so that the co-design method of robust Hfault-tolerant/attack-tolerant controller and event-triggered matrix was given out and the goal of co-design of the fault-tolerant and attack-tolerant control and the network communication was achieved. Finally, by means of simulative computational illustration, the effectiveness and feasibility of the theoretical result obtained were verified.