Completions of implicitly defined linear time varying vector fields

The stabilization of constraints through such techniques as Baumgarte stabilization has been used in the simulation community for some time. This and a number of control problems can be viewed as either extending, or modifying, a vector field off of some manifold. Generally these approaches required the equations to have a special structure. Motivated by numerical simulation there has recently been new progress on doing this stabilization in numerically robust ways for larger classes of systems. In this paper we point out how earlier linear time invariant results do not immediately apply to the linear time varying case and then analyze the linear time varying case.