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

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.

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Abstract:
Given an arbitrary initial value x₀^- for the differential-algebraic equation A x'(t)+B x(t) = f(t), an initial value x₀⁺ 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 x₀⁺ by means of a system of linear equations involving A, B, derivatives of f, and x₀^-, which gives a new method to numerically calculate x₀⁺.

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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