Output-based Event-holding Control in Presence of Measurement Noise

We present rules to stabilize the origin of a networked system, where data exchanges between the plant and the controller only occur when an output-dependent inequality has been satisfied for a given amount of time. This strategy, called Event-Holding Control (EHC), differs from time-regularized event-triggered control (ETC) techniques, which generate transmissions as soon as a triggering condition is verified and the time elapsed since the last transmission is larger than a given bound. Indeed, the clock involved in EHC is not running continuously after each transmission instant, but only when a criterion is verified. We propose an output-based design of these triggering mechanisms that are robust to additive measurement noise and ensure an input-to-state stability (ISS) property. This EHC scheme naturally has a positive lower bound on the transmission interval. Additionally, we show via an example that, in presence of measurement noise, Zeno-like behavior, where events are generated near the minimum inter-event time consistently, may occur when the system is close to the attractor. We introduce space-regularization to mitigate this issue, resulting in an input-to-state practical stability (ISpS) property rather than ISS.