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 h ave either considered linear equations or based their analysis on line ar equations. However, until very recently there has been little rigor ous investigation of the relationship between the linearization of a D AE and the original equations. In this paper we carefully examine seve ral aspects of this relationship. Positive results for time varying li nearization and counter examples for time invariant linearization are given.