This paper presents a new design concept of robust sensorless peak current-mode controlled DC-DC switching converters (SCs). Here we show that classical peak current-mode controlled SC (PCMCS) is under the class of slow-fast dynamical systems and that can be transformed into a reduced-order system using the notion of time-scale decomposition of a singularly perturbed system. Based on this decomposition, the reduced-order model of PCMCSs is derived and the composite state and disturbance observers are designed with the help of an equivalent-input-disturbance (EID) estimator. Moreover, rigorous stability criterion of closed-loop systems is provided to show the quantitative robustness between controller gains and parameter uncertainties. It is shown that the proposed design technique delivers a promising disturbance rejection property and an excellent dynamic performance with reduced hardware complexity. The feasibility of such approach is compared numerically with classical PCMCSs and then verified experimentally.