In this paper the Linear Constrained Regulation Problem without an assigned set of initial states is investigated. This problem consists of the determination of a linear state feedback control law and of a set of admissible initial states D, so that every trajectory of the resulting closed-loop system which emanates from the set D converges asymptotically to the origin without violation of the control constraints. By applying well-known results on the positive invariance of polyhedral sets, an eigenstructure assignment approach to this problem is established. If the number of unstable open-loop eigenvalues does not exceed the number of control variables, then this approach enables one to derive a linear state-feedback stabilizing control law which makes the set of states where the control constraints are respected positively invariant. This positively invariant set is the maximal admissible set of initial states for the control law under consideration. For the case where the number of control variables is greater than the number of the unstable open-loop eigenvalues, a modified algorithm is proposed.