  In this paper, we study feedback linearization problems for nonlinear
differential-algebraic control systems (DACSs). We consider two kinds of
feedback equivalences, namely, the external feedback equivalence, which is
defined (locally) on the whole generalized state space, and the internal
feedback equivalence, which is defined on the locally maximal controlled
invariant submanifold (i.e., on the set where solutions exist). Necessary and
sufficient conditions are given for the locally internal and the locally
external feedback linearizability of DACSs with the help of a notion called the
explicitation with driving variables, which attaches a class of ordinary
differential equation control systems (ODECSs) to a given DACS. We show that
the feedback linearizability of a DACS is closely related to the involutivity
of the linearizability distributions of the explicitation systems. Finally, we
apply our results of feedback linearization of DACSs to an academical example
and a constrained mechanical system.
