Growth bound of delay-differential algebraic equations

2013 ◽  
Vol 351 (15-16) ◽  
pp. 645-648
Author(s):  
Sébastien Boisgérault
Author(s):  
Ines Ahrens ◽  
Benjamin Unger

Abstract We present a graph-theoretical approach that can detect which equations of a delay differential-algebraic equation (DDAE) need to be differentiated or shifted to construct a solution of the DDAE. Our approach exploits the observation that differentiation and shifting are very similar from a structural point of view, which allows us to generalize the Pantelides algorithm for differential-algebraic equations to the DDAE setting. The primary tool for the extension is the introduction of equivalence classes in the graph of the DDAE, which also allows us to derive a necessary and sufficient criterion for the termination of the new algorithm.


2015 ◽  
Vol 2015 ◽  
pp. 1-6
Author(s):  
Leping Sun ◽  
Yuhao Cong

This paper is concerned with the asymptotic stability of delay differential-algebraic equations. Two stability criteria described by evaluating a corresponding harmonic analytical function on the boundary of a certain region are presented. Stability regions are also presented so as to show the method geometrically. Our results are not reported.


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