On inconsistent initial conditions for linear time-invariant differential-algebraic equations
On inconsistent initial conditions for linear time-invariant differential-algebraic equations
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关于线性时不变微分代数方程的不一致初始条件
DOI：
10.1109/iscas.2002.1010272
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发表时间：
2002
期刊：
影响因子：
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通讯作者：
P. I. Barton
中科院分区：
文献类型：
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作者：
G. Reissig;H. Boche;P. I. Barton
给定微分代数方程Ax/spl dot/（t）+Bx（t）=f（t）的任意初始值x/sub 0//sup -/，可以借助于拉普拉斯变换从该方程的所有一致初始值中选择初始值x/sub 0//sup +/。我们表明，这种选择是唯一一个满足一些简单的，物理上合理的假设线性系统的行为，从而排除了其他值的x/sub 0//sup +/在文献中提出的。我们的推导是基本的上述拉普拉斯变换为基础的方法相比，以前的理由：我们还特征化x/sub 0//sup +/通过一个系统的线性方程组，涉及A，B，f的导数，和x/sub 0//sup -/，这给出了一个新的方法来数值计算x/sub 0//sup +/。
Given an arbitrary initial value x/sub 0//sup -/ for the differential-algebraic equation Ax/spl dot/(t)+Bx(t)=f(t), an initial value x/sub 0//sup +/ can be selected from among all consistent initial values for that equation by means of the Laplace transform. We show that this choice is the only one that fulfils some simple, physically reasonable assumptions on linear systems' behavior, thereby ruling out other values of x/sub 0//sup +/ proposed in the literature. Our derivation is elementary compared to previous justifications of the above Laplace transform based method: We also characterize x/sub 0//sup +/ by means of a system of linear equations involving A, B, derivatives of f, and x/sub 0//sup -/, which gives a new method to numerically calculate x/sub 0//sup +/.