This paper proposes a methodology to design stabilising event-trigger strategies for PI-controlled linear continuous-time plants subject to input saturation. Using Lyapunov theory techniques, conditions based on linear matrix inequalities (LMI) are derived to guarantee regional (or global, when possible) asymptotic stability of the equilibrium. These conditions can be incorporated in optimisation problems to choose the parameters of the trigger function aiming at reducing the sampling activity, while ensuring the regional stability of the equilibrium with respect to a given set of admissible initial states. Simulation results illustrate the application and potentialities of the method.