Reachability and minimum energy control of positive 2D Roesser type models

A new class of positive 2D Roesser type models is introduced. Necessary and sufficient conditions are established for the reachability of the positive 2D Roesser type model for zero boundary conditions. It is shown that the positive 2D Roesser type model having not nilpotent system matrix is unreachable for nonzero boundary conditions. The minimum energy control problem is formulated and solved for the positive 2D Roesser type model with zero boundary conditions. It is shown that the reachability and controllability of positive linear 1D systems are not invariant under the state-feedbacks.