Linearization of DAEs along trajectories

Over the last decade there has been a considerable amount of research on numerical and analytic aspects of linear and nonlinear differential algebraic equations (DAEs)F(x', x, t, u)=0. Many of these papers have either considered linear equations or based their analysis on linear equations. However, until very recently there has been little rigorous investigation of the relationship between the linearization of a DAE and the original equations. In this paper we carefully examine several aspects of this relationship. Positive results for time varying linearization and counter examples for time invariant linearization are given.