SOLVABILITY OF GENERAL DIFFERENTIAL-ALGEBRAIC EQUATIONS

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.