In Chap.2, we consider discrete continuous systems with impulse controls. We give the general description of a nonlinear system with impulse control satisfying the robustness condition (self-consistency ), which is the synonym of robustness. We present analytic robustness conditions and define the discontinuous time change for robust discrete continuous system. The use of this method permits the representation of generalized or discontinuous solutions such as impulsive sliding modes, and subsequently the derivation of differential equations with a measure for this kind of solutions.