For the problems of limited bandwidth resources， the existence of external disturbance and parameter uncertainty， a non-fragile dissipative control scheme for event-triggered networked systems was proposed. Firstly， based on the Networked Control System （NCS） model， a non-periodic sampling event-triggered scheme was proposed， and a delay closed-loop system model was established. Then， a novel bilateral Lyapunov functional was constructed by using the structure characteristics of sawtooth wave. Finally， the sufficient conditions to ensure the stability of the system were derived by using methods such as Jensen inequality， free weight matrix and convex combination， and the gain of the feedback controller was calculated. The results of numerical simulation show that the proposed bilateral functional is less conservative than the unilateral functional， the event-triggered mechanism can save bandwidth compared with the common sampling mechanism， and the proposed controller is feasible.