Spatiotemporally asynchronous sampled-data control of a linear parabolic PDE on a hypercube

This paper employs the observer-based output feedback control technique to deal with the problem of spatiotemporally asynchronous sampled-data control for a linear parabolic PDE on a hypercube. By the spatiotemporally asynchronous sampled-data observation outputs, an observer-based output feedback control law is constructed, where the sampling interval in time is bounded. By constructing an appropriate Lyapunov–Krasovskii functional candidate and applying a weighted Poincaré–Wirtinger inequality on a hypercube, it is shown under a sufficient condition presented in terms of standard linear matrix inequalities that the suggested spatiotemporally asynchronous sampled-data control law asymptotically stabilises the PDE in the spatial (Formula presented.) norm but its convergence speed can be regulated by a known constant. Moreover, both open-loop and closed-loop well-posedness analysis are done within the framework of (Formula presented.) semi-group. Finally, numerical simulation results are presented to support the proposed design method.