Motivated by our prior research on automatic: aircraft guidance, we address stable inversion for output tracking and prove that this process is continuous with respect to parameter variations, even when these variations cause a change in relative degree. Our earlier simulations indicated that the stable inversion process is extremely accurate and that only a linear regulator about the desired trajectory is required in the face of reasonable modeling error. The principal novelty in our technique is that a differential equations point of view is taken as opposed to a state-space approach on the (driven) zero dynamics of the system. This is the situation that arises in many applications and it also enables handling the question of changes in relative degree, without having to be encumbered by the change in state space dimension as the parameters change. Linear systems are first studied, since the corresponding result is unknown. Next, a corresponding theorem for nonlinear systems proved by using the Picard process in conjunction with the result for the linear case. The principal contribution of this paper is a result concerning the continuous dependence of a generalized steady state solution of nonlinear driven differential equations, with respect to parameter variations which cause the order of the differential equation to change. Since the notion of steady state is of paramount importance to innumerable engineering situations, the contents of this paper have wider scope.