本文应用Maehly有理分式逼近方法得到了线性系统状态转移矩阵e~(A(?))的新算法。并给出了该算法的计算相对误差上界。由于使用了切比雪夫多项式,因此导出的算法几乎就是e~(A(?))在区间[a,b]内的最佳有理逼近。文中还给出了二阶系统的e~(A(?))计算机仿真结果,证实算法的结果对c~(A(?))有优良的逼近性。 In this paper, Maehly rational fractional approximation method is used to obtain a new algorithm for the state transition matrix e ~ (A (?)) Of a linear system. The upper bound of the relative error of the algorithm is given. Since Chebyshev polynomials are used, the derived algorithm is almost the best rational approximation of e ~ (A (?)) In the interval [a, b]. The e ~ (A (?)) Computer simulation results of the second order system are also given in this paper. It is proved that the result of the algorithm has good approximation to c ~ (A).