This paper deals with robust stabilization of a class of linear discrete-time systems under non-linear perturbations via output feedback. A bound on the non-linear perturbations is maximized in the design. It is shown that degree of freedoms by the introduction of instrumental variables employed in this paper lead to much flexibility in obtaining both a robust output feedback controller and a maximal allowable bound of the non-linear perturbations. An improved method involving linear matrix inequalities are suggested to solve the matrix inequalities characterizing a solution of the robust stabilization problem. Consequently, the proposed method can yield a much less conservative result than that of earlier methods. Of major interest is an extension to a class of interconnected systems composed of linear subsystems with non-linear interactions. A robust decentralized controller is presented such that the closed-loop systems are maximally tolerant to interconnected non-linear couplings. Numerical examples illustrate the validity of the proposed approach.