Title :
On inconsistent initial conditions for linear time-invariant differential-algebraic equations
Author :
Reißig, Gunther ; Boche, Holger ; Barton, Paul I.
Author_Institution :
Dept. of Chem. Eng., MIT, Cambridge, MA, USA
fDate :
11/1/2002 12:00:00 AM
Abstract :
Given an arbitrary initial value x0- for the differential-algebraic equation Ax˙(t)+Bx(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+.
Keywords :
Laplace transforms; linear differential equations; Laplace transform; arbitrary initial value; inconsistent initial conditions; linear systems; linear time-invariant differential-algebraic equations; Broadband communication; Chemical engineering; Chemical technology; Differential equations; Eigenvalues and eigenfunctions; Electronic mail; History; Laplace equations; Mobile communication; Terminology;
Journal_Title :
Circuits and Systems I: Fundamental Theory and Applications, IEEE Transactions on
DOI :
10.1109/TCSI.2002.804552