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In chemical, biological, or population (epidemiological) processes the feedback action may be considerably delayed by time-consuming chemical measurements or biological tests. With such large delays on the control action in mind, and motivated by the fact that in some of these systems only piecewise-constant inputs can be applied between time instants at which measurements trigger changes in control, we consider the problem of event-triggered stabilization of 1-D reaction–diffusion PDE systems with input delay. The approach relies on reformulating the delay problem as an actuated transport PDE which cascades into the reaction–diffusion PDE, and on the emulation of backstepping control. The paper proposes a static (state-dependent) triggering condition which establishes the time instants at which the control value needs to be updated. It is shown that under the proposed event-triggered boundary control, there exists a minimal dwell-time (independent of the initial conditions) between two triggering times which allows to guarantee the well-posedness of the closed-loop system, and the exponential stability. The stability analysis is based on Input-to-State stability theory for PDEs and small-gain arguments. A simulation example is presented to validate the theoretical results. [ABSTRACT FROM AUTHOR]

This paper aims at proposing a sufficient matrix inequality condition to carry out the global exponential stability of the wave equation under an event-triggering mechanism that updates a damping source term. The damping is distributed in the whole space but sampled in time. The well-posedness of the closed-loop event-triggered control system is shown. Furthermore, the avoidance of Zeno behavior is ensured provided that the initial data are more regular. The interest of the results is drawn through some numerical simulations. [ABSTRACT FROM AUTHOR]