scholarly journals Analysis and reformulation of linear delay differential-algebraic equations

2012 ◽  
Vol 23 ◽  
Author(s):  
Phi Ha ◽  
Volker Mehrmann
Keyword(s):  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Linear Delay ◽  
Delay Differential

scholarly journals Discontinuity Propagation in Delay Differential-Algebraic Equations

2018 ◽  
Vol 34 ◽  
pp. 582-601 ◽  
Author(s):  
Benjamin Unger
Keyword(s):  
Differential Algebraic Equations ◽  
Complete Characterization ◽  
Algebraic Equations ◽  
Case Scenario ◽  
Worst Case ◽  
Linear Delay ◽  
Method Of Steps ◽  
Matrix Pencils ◽  
Delay Differential ◽  
The Impact

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 pencils, 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 a worst-case scenario. Moreover, it reveals possible hidden delays in the DDAE and allows to study exponential stability of the DDAE based on the spectral abscissa. The new classification for DDAEs is compared to existing approaches in the literature and the impact of splicing conditions on the classification is studied.

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