Discontinuity propagation in delay differential-algebraic equations

Abstract: The propagation of primary discontinuities in initial value problems for linear delay differential-algebraic equations (DDAEs) is discussed. Based on the (quasi-) Weierstra{\ss} form for regular matrix pencil, a complete characterization of the different propagation types is given and algebraic criteria in terms of the matrices are developed. The analysis, which is based on the method of steps, takes into account all possible inhomogeneities and history functions and thus serves as the worst-case scenario. Moreover, it reveals possible hidden delays in the DDAE. The new classification for DDAEs is compared to existing approaches in the literature and the impact of splicing conditions on the classification is studied.