This paper presents an adaptive event-triggered control method for linear systems subject to input saturation. At the first, using convex hull properties, an observer-based controller is designed and then a generalized event-triggering mechanism is regarded. In order to extend more time interval between any two successive events, an adaptive event-triggered control method is also proposed. The proposed control methodology is based on finite-gain L2 stability. It is noteworthy that the proposed methods are designed in a co-design framework where the observer-based controller design with the event-triggering mechanisms are performed at the same time. Moreover, the presented adaptive approach offers more degrees of freedom as well as preserves the performance criteria high. Besides, Zeno avoidance analysis is studied by introducing a lower bound on inter-event times. Finally, the efficiency of the proposed methods is shown through a case-study numerical example.