Constrained controllability of discrete-time systems with additive disturbances

The constrained controllability of a discrete-time system with additive disturbances is considered where the control and the disturbance are termed admissible if they satisfy specified magnitude constraints. Constrained controllability is concerned with the existence of an admissible control which steers the state of the system to a given target set from a specified initial state for every admissible disturbance. It is shown that the disturbed system is constrained controllable if, and only if, an associated disturbance-free system is constrained controllable. Thus, existing results from the literature concerning the constrained controllability of disturbance-free systems can be used to check the constrained controllability of disturbed systems.