This article presents an observer‐based event‐triggering strategy for systems with slope‐restricted nonlinearities that depend on the state. Both the emulation and codesign problems are addressed. To avoid Zeno behavior, a minimum dwell time is considered. By using a looped‐functional approach and the cone‐bounded properties of the nonlinearity, sufficient conditions based on linear matrix inequalities are derived to ensure global asymptotic stability of the origin of the closed‐loop system under the proposed event‐triggering strategy. These conditions are incorporated into convex optimization problems to optimally determine the event‐triggering function parameters and the observer gain (in the codesign case) aiming at reducing the number of control updates. Numerical examples illustrate the potentialities of the approach.