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This paper presents a design method of static output feedback controllers that guarantees asymptotic stability for an extended plant of linear discrete-time systems with a periodic event-triggering condition based on the output error. The extended plant consists of an original plant and a filter that generates the input signal to the plant. Then the proposed static output feedback controller generates the auxiliary input from the triggered output signal of the plant. The design conditions proposed are reduced to convex conditions, while conventional design methods of static feedback controllers need some approximation. Numerical examples illustrate the effectiveness of the proposed event-triggered control.