Differential--Algebraic Equations of Index 1 May Have an Arbitrarily High Structural Index

Abstract

It is shown that the structural index of a linear {differential--algebraic equation} (DAE) with constant coefficients and with index 1 may be arbitrarily high, contrary to a previous result from the literature. This demonstrates that Pantelides' algorithm applied to DAEs of index 1 may perform an arbitrarily high number of iterations and differentiations.