Event-Based Boundary Control of a Linear $2\times 2$ Hyperbolic System via Backstepping Approach

In this paper, we introduce an event-based boundary control for a 2 × 2 coupled linear hyperbolic system. We use a well-established backstepping controller which stabilizes the system along with a dynamic triggering condition which determines when the controller must be updated. The main contributions rely on the definition of an event-based controller under which global exponential stability of the system is achieved and, furthermore, the existence of a minimal dwell-time between two triggering times is guaranteed. The well-posedness of the system under the event-based controller is stated. A simulation example is presented to illustrate the results.