Feasibility and stability of preview control for 2-D discrete-time systems described by the Roesser model

Feasibility and stability were deemed crucial for preview controller design in a two-dimensional (2-D) discrete-time (DT) system. In this paper, the feasibility and stability of preview control for the 2-D DT system described by the Roesser model with disturbances were studied. The underlying system involved the difference between a system state and its steady-state value, as opposed to the usual difference between system states typically utilized in past literature. An (AE) system was constructed in this paper, in which the augmented state variables not only contained error signals and preview information but also included a discrete integrator for the elimination of static errors. The AE system included a reference signal's future information and a disturbance signal to achieve the regulator problem from the existing tracking problem. Based on Lyapunov stability theory, a new linear matrix inequality (LMI)-based criterion was derived, ensuring the feasibility and stability of the derived AE system. Furthermore, a state feedback control law with a design approach of the preview control process was proposed based on the LMI method. The proposed controller was utilized to perform preview tracking control for the 2-D system while achieving the asymptotic stability of the overall closed-loop system. Finally, numerical examples were provided to demonstrate the advantages of the proposed method. MATLAB software and the yet another linear matrix inequality parser (YALMIP) toolbox were used to determine the controller gain matrix.