The paper presents an observer-based event-triggered control strategy for linear systems subject to input cone-bounded nonlinearities by using only available measurable variables. Sufficient conditions based on linear matrix inequalities are proposed to ensure the asymptotic stability of the closed loop and the avoidance of Zeno behavior in an emulation context. Based on these conditions, a convex optimization problem to compute the parameters of the event-trigger rule aiming at reducing the number of control updates is proposed. The approach is illustrated on a numerical example that considers the control of a linear system with a logarithmic input quantization constraint.