Network-based control of a semilinear damped beam equation under point and pointlike measurements

We consider distributed static output-feedback stabilization of a damped semilinear beam equation. Distributed in space measurements are either point or pointlike, where a pointlike measurement is the state value averaged on a small subdomain. Network-based implementation of the control law which enters the PDE through shape functions is studied, where variable sampling intervals and transmission delays are taken into account. Our main objective is to derive and compare the results under both types of measurements in terms of the upper bound on the delays and sampling intervals that preserve the stability for the same (as small as possible) number of sensors/actuators. For locally Lipschitz nonlinearities, regional stabilization is achieved. Numerical results show that the pointlike measurements lead to larger delays and samplings, provided the subdomains, where these measurements are averaged, are not too small.