  Robustness guarantees are important properties to be looked for during
control design. They ensure stability of closed-loop systems in face of
uncertainties, unmodeled effects and bounded disturbances. While the theory on
robust stability is well established in the continuous-time nonlinear
framework, the same cannot be stated for its discrete-time counterpart. In this
paper, we propose the discrete-time parallel of total stability results for
continuous-time nonlinear system. This enables the analysis of robustness
properties via simple model difference in the discrete-time context. First, we
study how existence of equilibria for a nominal model transfers to sufficiently
similar ones. Then, we provide results on the
