Background

Differential-algebraic equations (DAEs) are used to describe many physical problems. These types of equations arise for instance in the modelling of electrical networks, opti-mal control, mechanical systems, incompressible fluids and chemical process simula-tions. An important quantity that characterizes DAEs and which plays a key role in the treatment of these equations is the index. There are various definitions for the index of a DAE (Martinson and Barton 2000; Günther and Wagner 2001; Rang and Angermann 2005; Kunkel and Mehrmann 1996) but the most used one is the differentiation index. It is defined as the minimum number of times that all or part of the DAE must be differen-tiated with respect to time, in order to obtain an ordinary differential equation (Martin-son and Barton 2000). Higher-index DAEs (differentiation index greater than one) arise naturally in many important application problems. For instance, they model constrained multibody systems (Simeon 1993, 1996; Benhammouda and Vazquez-Leal 2015), vehi-cle system dynamics (Simeon et al. 1991, 1994), space shuttle simulation (Brenan 1983) The solution of higher-index Hessenberg differential-algebraic equations (DAEs) is o