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Abstract Periodic event‐triggered control (PETC) evaluates triggering conditions only at periodic sampling times, based on which it is decided whether the controller needs to be updated. This article investigates the global stabilization of nonlinear systems that are affected by external disturbances under PETC mechanisms. Sufficient conditions are provided to ensure the resulting closed‐loop system is input‐to‐state stable (ISS) for the state feedback and the observer‐based output feedback configurations separately. The sampling period and the triggering functions are chosen such that the ISS‐Lyapunov function of continuous dynamics is also the ISS‐Lyapunov function of the overall system. Based on that, sufficient conditions in the form of linear matrix inequalities are provided for the PETC design of incrementally quadratic nonlinear systems. Two simulation examples are provided to illustrate the effectiveness of the proposed method.