A design techique for the control of discrete-time systems subject to state and control constraints

The regulation problem of linear discrete-time systems under state and control constraints is investigated. In the first part of the paper necessary and sufficient conditions for the existence of a solution to the constrained control problem are established. The constructive form of the proof of this result provides also a method for the derivation of a control law transferring to the origin any state belonging to a given set of initial states while respecting the state and control constraints. Then a design technique for the determination of a solution to the constrained control problem is developed. The proposed technique is based on the reduction of the constrained control problem to simple linear programming problems.