A Lyapunov Function Approach to the Event-triggered Stabilization of the Minimal Robust Positively Invariant Set

Abstract

Abstract: We propose an event-triggered controller for linear discrete-time systems subject to bounded additive disturbances. For such systems under linear stabilizing control (updated at every sampling instant), it is known that the compact set which is minimal among all robust positively invariant sets is stabilized. We define an event condition based on a Lyapunov function for this minimal robust positively invariant set. As this set can in general not be represented with finite complexity, we provide means to approximate the Lyapunov function in question. Further, in order to reduce the number of events, we employ a relaxed decrease condition on the Lyapunov function in the event condition, merely requiring the decrease over multiple time steps and not from every time step to the next.