Positivity and stabilization of 2D linear systems with delay

The problem of finding a gain matrix of the state-feedback of 2D linear system with delays such that the closed-loop system is positive and asymptotically stable is formulated and solved. Necessary and sufficient conditions for the solvability of the problem are established. A procedure for computation of the gain matrix is given and illustrated by numerical example. The proposed approach is demonstrated on 2D linear system described by the general 2D model but it can be extended to 2D linear system described by the 2D Roesser model.