Observer-based event-triggered boundary control of a linear 2 × 2 hyperbolic systems

International audience ; This paper deals with an observer-based event-triggered boundary control for a coupled 2×2 linear hyperbolic system. The approach builds on an output feedback controller depending on estimated states along with a dynamic triggering condition which establishes the time instants at which the control value needs to be sampled/updated. This work combines some recent results on boundary stabilization via the backstepping approach with some event-triggered control strategies for this kind of PDE system. In this paper, it is shown that under the proposed event-triggered boundary control, there exists a minimal dwell-time (independent on initial conditions) between two triggering times and furthermore the well-posedness and global exponential stability are guaranteed. A simulation example is presented to validate the theoretical results with further discussions on the advantages of the proposed scheme.