Stability analysis and design of an event-triggered control scheme for a coupled ODE-heat PDE system.

This paper tackles the stability analysis of a system driven by linear ordinary differential equation coupled to a one-dimensional heat equation. The particularity of this study concerns the nature of the coupling, which is performed using an event-triggered scheme, through a boundary condition of the partial differential equation. After proving the existence and regularity of solutions of the system, the idea is to introduce an enriched energy functional as a candidate Lyapunov functional to prove the exponential stability. Actually, we will obtain a sufficient stability condition expressed as a linear matrix inequality to satisfy. This condition is suitable for solving an emulation problem corresponding to the appropriate tuning of the event-triggered control. Our result is finally illustrated with a numerical example.