For linear systems, the robust control under the event-triggered optimization mechanism is analyzed. Firstly, on basic of time-triggering and event-triggering mechanism, the system optimization performance index is given and the optimized controller is designed. When the external interference is zero, the proof of the asymptotic stability of the linear systems is given. When the external interference is not zero, the system has interference suppression level γ of $H_{\infty}$ control. Then, the Zeno behavior of the linear system is analyzed, and a positive minimum event-triggering time interval is given by derivation. Finally, system simulation demonstrates the proposed algorithm's correctness.