In this paper, a new event-switched control method is presented for controlling discrete-time linear systems subject to bounded disturbances. With this method, the nominal performance of the controlled system can be maintained although the control law does not have to be systematically updated. The feedback control loop can be opened as long a state-dependent event condition is satisfied. This condition is obtained using set theory approaches. In particular, the concept of robustly positive invariant sets is used to calculate the nominal performance and the event condition. The simulation presented and discussed here confirms the efficiency of the present approach. Issues relating to the real-time implementation of this approach are also discussed.