e^(At)四种计算方法的比较

Comparison with four Methods of Calculation for e^(At)

状态转移矩阵eAt在现代控制理论与工程技术以及常系数微分方程组理论中有着非常重要的应用.通过一个实例,给出计算状态转移矩阵eAt的四种不同的方法:矩阵指数函数展开法,Jordan标准形法,待定系数法,Laplace变换法.笔者论述了各种计算方法的基本步骤及计算的难点与要点,经过分析对比,最后给出最优选择.

The etate transfer matrix e^At is very important in mordern cybertics, engineering technique, and in the theory of linear differential systems of equations with constant coefficients. In this paper for an example four methods for calculating e^At are given . The four methods are the expansion method of matric exponential function, the method of Jordanian canonical form, the method of undetermined coefficients, and Laplacian transformation approach. The penner discusses the fundamental steps, analyses the difficult place and the main points of all methods. With anaylsis and comparation the optimal selection is obtained at last.