The differential models from Section 13.1 may seem unrealistic in many applications because actions are required to undergo instantaneous changes. For example, in the simple car, the steering angle and speed may be instantaneously changed to any value. This implies that the car is capable of instantaneous acceleration changes. This may be a reasonable approximation if the car is moving slowly (for example, to analyze parallel-parking maneuvers). The model is ridiculous, however, at high speeds.
Suppose a state transition equation of the form is given in which the dimension of is . The model can be enhanced as follows: