Gunther Reißig,
Holger Boche, and Paul I. Barton.

On inconsistent initial conditions for linear time-invariant
differential-algebraic equations.

IEEE Trans. CAS, Part I, vol. 49, no. 11, Nov. 2002, pp. 1646-1648.

Full text.
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**Abstract:**

Given an arbitrary initial value x_{0}^{-} for the differential-algebraic equation
A x'(t)+B x(t) = f(t), an initial value x_{0}^{+} can be selected from among all
consistent initial values by means of the Laplace transform.
We show that this choice is the only one that fulfills some simple, physically reasonable
assumptions on linear systems' behavior.
Our derivation is elementary compared to previous justifications
of the above Laplace transform based method.
We also characterize x_{0}^{+} by means of a system of linear equations involving
A, B, derivatives of f, and x_{0}^{-},
which gives a new method to numerically calculate
x_{0}^{+}.

**BibTeX entry:**

@article{ReissigBocheBarton02,
AUTHOR = {Rei{\ss}ig, Gunther and Holger Boche and Paul I. Barton},
TITLE = {On inconsistent initial conditions for linear time-invariant differential-algebraic equations},
JOURNAL = {IEEE Trans. Circuits Systems I Fund. Theory Appl.},
VOLUME = {49},
YEAR = {2002},
NUMBER = {11},
PAGES = {1646-1648},
doi = {10.1109/TCSI.2002.804552}
}

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