On the admissibility and robust stabilization of 2D singular continuous–discrete linear systems

The effectiveness of this paper lies in the investigation of admissibility in 2D singular continuous–discrete time linear systems described by the Roesser model. Its objective is to examine if, how and when the conditions of admissibility and robust admissibility are satisfied. To achieve this study, sufficient conditions were defined and used to measure the admissibility and the robust admissibility of this class of systems. Moreover, we have derived sufficient conditions for the existence of a state feedback controller that guarantees that closed-loop systems are admissible and robustly admissible. Finally, some numerical examples which discuss the Darboux equation, spatially interconnected systems (ladder circuits) and an academic example are provided to demonstrate the accuracy and applicability of the proposed results.