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For a networked control system (NCS), this article proposes a more configurable event triggering control scheme that employs a finite memory structure with tuning parameters for efficiently utilizing network resources in transient and steady-state responses. The proposed finite memory event triggering control scheme (FMETS) uses the current and past states on the recent finite time horizon to asymptotically stabilize a closed-loop system. Tuning parameters can be configured according to the forgetting level, the triggering threshold, and the memory size. Since the FMETS takes a sample-and-hold approach, the undesirable Zeno effect can be avoided automatically. To use an efficient computation solver, the proposed FMETS is formulated into linear matrix inequalities (LMIs). It is shown through a simulation study that the proposed FMETS provides less conservative results and furthermore enables effective configuration for high control performance and efficient network resource utilization.