Design techniques 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 regulation problem are established. The constructive form of the proof of this result also provides 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. In the second part of the paper, design techniques are proposed in which the determination of the control law is reduced to simple linear programming problems