Event-Triggered Finite-Dimensional Observer-Based Output Feedback Stabilization of Reaction–Diffusion PDEs

This article addresses the topic of event-triggered output feedback stabilization of reaction–diffusion partial differential equations (PDEs). The control applies at the boundary while the output is distributed. The control strategy consists of a finite-dimensional controller augmented with an adequate event-triggered mechanism. This event-triggered mechanism dictates the time instants at which the applied control input needs to be updated based on the occurrence of specific events monitored by the control law. The reported stability analysis relies on the use of two small gain arguments. A first small gain argument is used to establish that the employed finite-dimensional observer-based control strategy with continuous application of the control input (i.e., without triggering mechanism) satisfies an input-to-state stability (ISS) estimate with respect to an additive perturbation of the control input. Then, taking advantage of this latter ISS estimate along with the introduction of an adequate triggering mechanism, a second small-gain argument is developed to establish the exponential decay of the resulting closed-loop system trajectories. Finally, the feasibility of the reported event-triggered control approach is assessed through the establishment of a minimal dwell-time between two triggering instants.