Input-to-state stability of self-triggered control systems

Event-triggered and self-triggered control have recently been proposed as an alternative to periodic implementations of feedback control laws over sensor/actuator networks. In event-triggered control, each sensing node continuously monitors the plant in order to determine if fresh information should be transmitted and if the feedback control law should be recomputed. In general, event-triggered control substantially reduces the number of exchanged messages when compared with periodic implementations. However, such energy savings must be contrasted with the energy required to perform local computations. In self-triggered control, computation of the feedback control law is followed by the computation of the next time instant at which fresh information should be sensed and transmitted. Since this time instant is computed as a function of the current state and plant dynamics, it is still much larger than the sampling period used in periodic implementations. Moreover, no energy is spent in local computations at the sensors. However, the plant operates in open-loop between updates of the feedback control law and robustness is a natural concern. We analyze the robustness to disturbances of a self-triggered implementation recently introduced by the authors for linear control systems. We show that such implementation is exponentially input-to-state stable with respect to disturbances.