Structural analysis in differential-algebraic systems and combinatorial optimization

In this paper we consider the structural analysis problem for differential-algebraic systems with conditional equations. This problem consists, given a conditional differential algebraic system, in verifying if the system is well-constrained for every state, and if not to find a state in which the system is bad-constrained. We give a formulation for this problem as an integer linear program. This is based on a transformation of the problem to a matching problem in an auxiliary graph. We also show that the linear relaxation of that formulation can be solved in polynomial time. Using this, we develop a branch-and-cut algorithm for solving the problem.