This paper addresses the problem of static output control design for a class of discrete-time ostensible positive linear systems, characterized by parametric boundaries within the required application of the diagonal stabilization principle. Given these basic constraints, a static output control parameterization for this class of linear systems is derived, which complements the condition for asymptotic stability of the closed-loop system defined using the Lyapunov method. The set of linear matrix inequalities used is conditioned by linear matrix equality to remove the existing bilinearity in the matrix inequalities and to guarantee a strictly positive gain for the control law. The side benefit is the creation of an adequate synthesis methodology, formulated within the paradigm of linear matrix inequalities. The proposed approach is illustrated related to the motivating applications.