On L_p-gains in Noisy Event-triggered Control

This paper investigates the design of event-triggered control strategies that guarantee ${\mathcal{L}}_{p}$-stability properties when measurement noise is present. It is well known that in many event-based transmission schemes, the inclusion of measurement noise can lead to the so-called Zeno phenomenon, where an infinite number of transmissions occur in a finite amount of time, even when a minimum inter-event time is guaranteed in absence of noise. In this paper, we present a solution to the open problem of designing triggering rules, which ensure bounded ${\mathcal{L}}_{p}$-gains from the exogenous inputs to a desired performance output in the closed-loop system, in the presence of measurement noise. We guarantee a global minimum inter-event time by design. Additionally, we show that suitable choices of the tuning parameters allow us to affect the “steady-state” inter-event times (when close to the attractor) by exploiting the design freedom in the parameter selection, which may result in improved behavior when close to the attractor. We showcase our results through a consensus example.