On the conditions of limited sets of reachability and controllability for linear systems with discrete time and total first-order constraints on scalar control

The article discusses linear systems with discrete time and summary constraints on first-order scalar control. For this class of systems, the reachable and null-controllable sets in a finite number of steps and their limit analogues are studied. The criterion for the boundedness of reachable and null-controllable limit sets in terms of matrices of the system is formulated and proved. In the case of their boundedness, the conditions under which the studied sets are polyhedra are determined. The structure of polyhedra is defined. Examples are presented, and numerical modeling of reachable and null-controllable sets of various systems is carried out.

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