Static output feedback control for positive 2D discrete systems in Roesser model

Abstract This paper investigates the output stabilization problem for multi-input multi-output positive 2D systems described by a linear discrete-time Roesser system. This kind of systems have the property that the horizontal and vertical states take non-negative values whenever the initial boundaries are non-negative. Conditions for the existence of desired static output feedback controllers guaranteeing the resultant closed-loop system to be positive and asymptotically stable are obtained. Also, the synthesis of static output feedback controllers, including the requirement of positivity of the controllers, is solved. These results are then extended to the case of uncertain plants. All of the proposed conditions are expressed in terms of Linear Programming, which can be easily verified by using standard numerical software. Finally, several numerical examples are included to illustrate the validity and the effectiveness of the developed results.