This paper investigates the problem of event-triggered control for semi-global stabilisation of null controllable systems subject to actuator saturation. First, for a continuous-time system, novel event-triggered low-gain control algorithms based on Riccati equations are proposed to achieve semi-global stabilisation. The algebraic Riccati equation with a low-gain parameter is utilised to design both the event-triggering condition and the linear controller; a minimum inter-event time based on the Riccati ordinary differential equation is set a priori to exclude the Zeno behaviour. In addition, the high-low gain techniques are utilised to extend the semi-global results to event-based global stabilisation. Furthermore, for a discrete-time system, novel low-gain and high-low-gain control algorithms are proposed to achieve event-triggered stabilisation. Numerical examples are provided to illustrate the theoretical results.