Gunther Reißig.

Differential-Algebraic Equations and Impasse Points.

IEEE Trans. CAS, Part I, vol. 43, no. 2,
Feb. 1996, pp. 122-133.

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text. (Definitive publication; restricted access).

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**Abstract:**

Impasse points can occur in the analysis of
Differential-Algebraic Equations (DAEs) that, for example,
describe the dynamic behavior of electrical networks. Such
points are usually characterized by the condition that solutions
of the DAE in question cannot be continued beyond them. However,
it turns out that several classes of impasse points, each of
which represents different behavior of the DAE, do exist. In
this paper, relations between these classes and between impasse
points and pseudo limit points are examined for the first time.
Sufficient conditions as well as necessary conditions for a
point to be an impasse are given. Known results similar to ours
are restricted to the class of forward and backward impasse
points and concern continuously differentiable solutions only. We
extend and generalize them; some become special cases of theorems
in this paper. Other results are disproved by our
counterexamples.

**BibTeX entry:**

@article{Reissig96,
AUTHOR = {Rei{\ss}ig, Gunther},
TITLE = {Differential-algebraic equations and impasse points},
JOURNAL = {IEEE Trans. Circuits Systems I Fund. Theory Appl.},
VOLUME = {43},
YEAR = {1996},
NUMBER = {2},
PAGES = {122-133},
doi = {10.1109/81.486434}
}

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