Combinatorial optimization model and MIP formulation for the structural analysis of conditional differential‐algebraic systems

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 structurally nonsingular for every state, and if not in finding a state in which the system is structurally singular. We give a formulation for this problem as an integer linear program. This is based on a transformation of the problem into 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 and present some experimental results.