In this paper the comparison principle is applied to the design of feedback controllers for nonlinear discrete-time systems subject to physical constraints. First, the connection between the comparison principle and the existence of positively invariant sets of a special form is established and polyhedral positively invariant sets for nonlinear systems are obtained. Then these results are applied to the determination of state feedback control laws that transfer to the origin all initial states of a prespecified region of the state-space without violation of physical constraints on the control vector.