This paper deals with the design of an event-triggering mechanism using local information for a linear system controlled by an observer-based feedback controller. The event-triggered control strategy is based on a new dynamic triggering mechanism, which is introduced through an internal dynamic variable. Sufficient conditions based on linear matrix inequalities are proposed to ensure the asymptotic stability of the closed loop together with the avoidance of Zeno behavior. A convex optimization problem leans on these conditions to determine the parameters of the event-trigger rule aiming at reducing the number of control updates. Discussion with respect to the simpler state feedback case is drawn.