Reachability and controllability of non-negative 2-D Roesser type models.

*(English)*Zbl 0888.93009Linear discrete 2-D systems with nonnegative constant coefficients are considered. Using the general response formula for discrete 2-D Roesser type systems, a necessary and sufficient pure algebraic condition for reachability in a given rectangle is formulated and proved. It is shown, that for nonzero boundary conditions discrete 2-D systems are uncontrollable and unreachable in a finite given rectangle. Moreover, several remarks and comments on controllability and reachability of discrete 2-D linear systems are given. The paper extends to the 2-D case the results which are known for 1-D discrete linear systems. Finally, let us mention that similar problems for 2-D linear discrete systems have been recently considered in the monograph [J. Klamka, Controllability of Dynamical Systems (1991; Zbl 0732.93008)] and in the paper [J. Klamka, Appl. Math. Comput. Sci. 7, No. 4, 101-120 (1997)].

Reviewer: J.Klamka (Katowice)