Sl. Campbell et E. Griepentrog, SOLVABILITY OF GENERAL DIFFERENTIAL-ALGEBRAIC EQUATIONS, SIAM journal on scientific computing, 16(2), 1995, pp. 257-270
In the last few years there has been considerable research on differen
tial algebraic equations (DAEs) f(t,x,x') = 0 where f(x') is identical
ly singular. Most of this effort has focused on computing a solution t
hat is assumed to exist. That is, the DAE is assumed solvable. More re
cently there have been existence results developed using differential
geometry. For complex higher index systems these characterizations can
be hard to verify in practice. In this paper the computational verifi
cation of solvability is investigated. This first requires developing
an alternative set of sufficient conditions for solvability which are
more amenable to computation. Verification of these conditions using r
eadily available numerical and symbolic software is then discussed. An
example from robotics where classical graph theoretical approaches gi
ve an incorrect answer is worked to illustrate the usefulness of the s
ufficient condition and the computational approach.