The present paper has two main purposes. The first is to provide an explicit state-space solution of the robust stabilization problem with respect to the NLCF for two-time scale systems. In this construction only the solutions of the control and of the filtering Riccati equations associated with the slow and with the fast dynamics of the nominal plant are used. These solutions do not depend upon the singular perturbation and therefore all computations are well-conditioned. The second purpose of the paper is to investigate the case when an epsilon-independent robust controller can be used for the robust stabilization of a two-time scale nominal system. Two constructions of such controllers are developed under some additional assumptions. Numerical examples illustrate the theoretical developments.