In Chap.4, we present a general concept of the generalized (discontinuous) solutions in optimal control problems. We describe the discontinuous time-change method for general nonlinear control systems with ordinary and impulse controls, for both robust and non-robust discrete continuous systems with impulse control. We review systems with linear dependence on an unbounded control and derive a representation of the jumps of trajectories for this class of systems in full detail. This chapter establishes a bridge between the “naive” description of discrete continuous systems and systems with impulsive controls.