Based on Euler's methodology, we present a new discretization scheme of two-time-scale non-linear continuous-time systems. This scheme of the discretization consists in using two periods, slow and fast, which are determined with respect to slow and fast variables rate respectively, and allows us to define and then implement a multirate digital control for such systems to cope with this multirate measurements on-line. To this end, two reduced order observers are constructed for the slow and fast subsystems by referring to the knowledge of the left-inversion of the state-to-measurements map problem.