No abstract

In this paper, we introduce a new policy defining a stabilizing event-based controller for linear time-invariant systems. The plant operation is divided into two phases, a transient phase and a steady-state regime. In transient regime, we define a Lyapunov-like function; a positive definite function that vanishes only at the origin. However, while a regular Lyapunov function is decaying in time, the Lyapunov-like function is allowed to increase, provided that it remains bounded, in order to get larger inter-event times. An upper threshold is thus fixed in the form of an exponentially decaying function, the rate of decay of which is set by solving a generalized eigenvalue problem. In the vicinity of the steady state, the Lyapunov function is prevented from increasing in time to ensure a faster convergence with less control updates.

Event-based control techniques are investigated for output reference tracking in the case of linear time-invariant systems. In event-based control, the controller remains at rest if the system is behaving according to some predefined conditions, the feedback loop being closed only when the system states violate these conditions. In this work a reference system, which consists in the continuously-controlled version of the system under study, is employed. Based on the difference between the state of the event-triggered system and that of the reference system, we define a Lyapunov-like function, and show that if we can keep this function confined to a certain region, the tracking error would also be bounded. The trespassing of this function outside of the desired region is used as an event-triggering condition.