Event-Triggered Output Feedback Stabilization of Coupled Linear Parabolic PDE-ODE System

In this paper, we deal with an event-triggered output-feedback boundary control of an ODE system coupled with a heat equation. An observer-based controller for the continuous control input is designed. Motivated by it, an observer-based event-triggered controller is proposed, which is obtained by sampling the observer-based continuous-time controller. A dynamic event triggering mechanism (ETM) is introduced to determine the updating times of the actuation signal. The exponential stability in the event-based closed-loop system is proved via Lyapunov method. Moreover, a minimal dwell-time exists between any two triggering times, which means that the absence of a Zeno behavior.