On the Maximal Output Admissible Set for Linear Distributed Systems

This paper investigates the maximal output set for a class of linear distributed systems with discrete output. This exploration is novel, as previous studies primarily focused on localized systems. We define an initial state as output admissible if its corresponding output satisfies specified constraints. This set of initial states termed the maximal output set (MOS), is shown to be nonempty, bounded, and characterized by a finite number of inequalities under suitable assumptions. In addition to theoretical characterization, we propose an algorithmic approach. To illustrate our framework, we provide a numerical example involving a parabolic system. Furthermore, we apply our results to address a disturbance rejection problem, aiming to design feedback controls that ensure the robustness of the system's output against disturbances.