In this paper, we investigate the stability of a controlled system in the event-triggering framework. By designing the triggering scheme, the control signals are updated when it is demanded subject to some satisfactory system performance. However, the stability of the system is not yet fully investigated with respect to the triggering conditions. So, the main purpose of the paper is to analyse the stability of the system with respect to the proposed triggering scheme. In this paper, sliding mode control (SMC) is used to design the event-triggered control. Our analysis proposes a new notion called bounded event property for the event which guarantees the triggering instants are generated in finite-time for all possible values of the triggering parameter. It is shown that the event-triggered SMC ensures possess the bounded event property and moreover the proposed triggering mechanism also guarantees the stability of the closed loop system stability. © 2018 IEEE.