We consider the following problems. Given a discrete-time linear system, find, if possible, linear state-feedback control laws such that the corresponding closed-loop system trajectory is positive whenever the initial state is positive. This problem is called the feedback holdability problem. If, in addition, the requirement of non-negativity is imposed on controls, the problem is a positive feedback holdability problem. In the paper, necessary and sufficient conditions for feedback and positive feedback holdability are established in a form of systems of linear inequalities and a procedure for computing the set of all state-feedback controllers that make the closed-loop system holdable is proposed. The relation between controllability and holdability is also treated. Feedback and positive feedback holdability of the class of positive systems is considered as well.