ISS output feedback synthesis of disturbed reaction–diffusion processes using non-collocated sampled-in-space sensing and actuation

Linear proportional ISS synthesis of parabolic systems is developed within the practical framework of in-domain embedded sensing and actuation. The underlying system is affected by external disturbances and it is governed by a non-homogeneous reaction–diffusion PDE with a priori unknown spatially varying parameters. The present investigation focuses on practically motivated sampled-in-space sensing and actuation. A finite number of available sensing and actuating devices are assumed to be located along the one-dimensional spatial domain of interest. Tuning of the controller gains is then constructively developed by means of the Lyapunov approach to achieve a desired attenuation level for external distributed disturbances, affecting the system in question. Dual observer design is additionally developed within the present framework, and it is involved into the non-collocated output feedback synthesis. Theoretical results are supported by simulations made for the proposed synthesis over non-collocated sensing and actuation.