Reachability and controllability of 2-D Roesser model with bounded inputs

The notion of U-controllability introduced by Klamka (1994) is extended to the U-reachability and U-controllability of a 2-D Roesser model. Necessary and sufficient conditions for U-reachability and U-controllability of 2-D Roesser models are established. It is shown that: (1) the 2-D Roesser model and general 2-D model with nonnegative parameters are always U-unreachable; (2) the U-reachability of the 2-D Roesser model always implies its U-controllability; (3) if the system matrix of the 2-D Roesser model is nonsingular then the U-controllability also implies its U-reachability; and (4) the 2-D Roesser model with bounded inputs is not locally reachable and locally controllable if the norm of its system matrix is less or equal to one