On the standard canonical form of time-varying linear DAEs
On the standard canonical form of time-varying linear DAEs
复制标题
时变线性 DAE 的标准规范形式
DOI：
--
复制
发表时间：
2012
期刊：
影响因子：
--
通讯作者：
A. Ilchmann
中科院分区：
文献类型：
--
作者：
T. Berger;A. Ilchmann
本文给出了时变线性微分代数方程E（t）x = A（t）x的解的理论，该方程可以转化为标准标准型，即微分代数方程解耦为一个常微分方程z1 = J（t）z1和一个纯微分代数方程N（t）z2 = z2，其中N是逐点严格下三角形的.此类是时不变DAE的时变推广，其中相应的矩阵束是正则的。它将显示在何种意义上的SCF是一个标准形式，它允许一个过渡矩阵类似的常微分方程，以及如何利用这可以得到一个常数公式的变化。此外，我们证明了在这个意义上的系统转移到SCF是等价的DAE是解析可解的，并与SCF的衍生阵列的方法，dierentiation指数和奇异性指数。最后给出了一个确定DAE到SCF的转换矩阵的算法。
We introduce a solution theory for time-varying linear dierential-algeb raic equations (DAEs) E(t) _ x = A(t)x which can be transformed into standard canonical form (SCF), i.e. the DAE is decoupled into an ODE _ z1 = J(t)z1 and a pure DAE N(t) _ z2 = z2, where N is pointwise strictly lower triangular. This class is a time-varying generalization of time-invariant DAEs where the corresponding matrix pencil is regular. It will be shown in which sense the SCF is a canonical form, that it allows for a transition matrix similar to the one for ODEs, and how this can be exploited to derive a variation of constants formula. Furthermore, we show in which sense the class of systems transferable into SCF is equivalent to DAEs which are analytically solvable, and relate SCF to the derivative array approach, dierentiation index and strangeness index. Finally, an algorithm is presented which determines the transformation matrices which put a DAE into SCF.