e^(Ax)的Thiele型矩阵有理逼近

Thiele's matrix rational approximation of e^(Ax)

矩阵指数函数eAx的计算在线性系统理论及半群理论中有着特殊的作用,在现代控制理论中,无论是齐次方程还是非齐次方程的求解,主要取决于矩阵指数函数eAx的计算和近似。文章利用代数知识给出了矩阵指数函数eAx的连分式逼近函数的一个重要性质和定理,并在此基础上对矩阵指数函数eAx的连分式算法进行改进,最后用数值例子来验证其可行性。

Calculating the functions of the matrix exponential e^Ax has special significance in the theory of linear systems and the theory of semi-groups. Especially, in the modern control theory, no matter the equation is homogeneous or non-homogeneous, the result depends on the calculation of the matrix exponential e^Ax. In this paper, an important property and a theorem have been given about the matrix Thiele＇s continued fraction which is used to approximate the function of e^Ax. Based on the property, the Thiele algorithm is improved. A numeral example is also provided.