SOLUTION OF A LINEAR DIFFERENTIAL EQUATION IN THE FORM OF POWER SERIES AND ITS APPLICATION
SOLUTION OF A LINEAR DIFFERENTIAL EQUATION IN THE FORM OF POWER SERIES AND ITS APPLICATION
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幂级数形式的线性微分方程的解及其应用
DOI：
10.1142/9789812799661_0005
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发表时间：
2001
期刊：
影响因子：
--
通讯作者：
T. Kitamoto
中科院分区：
文献类型：
--
作者：
T. Kitamoto
设为一个包含参数qi（i = 1，2，.，k）的矩阵。给定一个线性微分方程$$ \left\{ \开始{array}{ccc} \displaystyle\frac{d}{dt} x（t）& = & Ax（t）}\\[8 pt] x（0）& = & x_0 \end{array}\right\，，\eqno{（1）} $$其中是一个维向量，一般很难显式计算解。在本文中，我们计算的解的截断幂级数的形式在t-t0和qi，其中t0是一个给定的常数。我们应用该方法的控制系统的设计。结果表明，设计参数的确定可以考虑被控系统的时间响应，简化了设计过程。
Letbe anmatrix which contains parameters qi(i = 1, 2, …, k). Given a linear differential equation $$ \left\{ \begin{array}{ccc} \displaystyle\frac{d}{dt} x(t) & = & Ax(t)}\\[8pt] x(0) & = & x_0 \end{array}\right\,, \eqno{(1)} $$ whereis an-dimensional vector, it is generally difficult to compute solutionexplicitly. In this paper, we compute the solution in the form of truncated power series in t - t0and qi, where t0is a given constant number. We apply the method to a control system design. It is shown that design parameters can be determined in consideration of the time response of controlled system, which simplifies the design process.