We investigate event-triggered observer design for infinite-dimensional dynamical systems governed by partial differential equations. The proposed framework combines a Lyapunov-based analysis with careful estimates on the observer dynamics, allowing us to derive uniform bounds on the state reconstruction error. A central difficulty lies in the coupling between the observer and the triggering mechanism, which may lead to an accumulation of triggering times. We address this issue by establishing bounds that are independent of the triggering sequence, ensuring a strictly positive minimum inter-event time.

We consider a class of linear systems for which a Luenberger-type observer is available and propose a dynamic event-triggering mechanism that determine when the control input should be updated.

Unlike approaches that rely on state-dependent triggering rules, our conditions are formulated using the observer state only, making them implementable in practice when full-state measurements are unavailable.

The dynamic rule incorporates an internal variable that provides additional flexibility in preventing event accumulation.

Under suitable assumptions, we prove exponential stability of the closed-loop system and we give sufficient conditions for the triggering times not to accumulate on finite-time horizon excluding Zeno behaviour.

Furthermore, the operator generating the system dynamics is not assumed to be skew-adjoint, which broadens the applicability of our approach to systems with quasi-dissipative or non-conservative behaviour.

Beyond the theoretical contribution, we mention how these results provide a natural and efficient tool for real-time state reconstruction and control of large-scale dynamical systems, in particular transportation networks.