The problem of stabilization of single-input single-output discrete-time periodic systems subject to input constraint is discussed in this paper. Precisely, the initial state of the system is assumed to belong to a given polyhedron and the scalar input is constrained to be bounded. It is shown how this problem can be posed in terms of the polynomial description of the system. The solution can be found by using a linear programming optimization algorithm. (C) 2003 Elsevier Ltd. All rights reserved.