线性状态方程的精确计算

Precision calculation of linear state equations

以解析法为基础，采用新的精确计算方法求解线性系统的状态方程．该方法属于一种２Ｎ类算法，它是把每一时间步长再进一步细分为２Ｎ个精细步长，然后在精细步长内利用泰勒展开式求解矩阵函数．与传统的Ｒｕｎｇｅ－Ｋｕｔａ方法比较，这种方法兼有解析法与数值法的优点，稳定性好，可以采用较大的时间步长以提高计算效率．

Anew precision method, a kind of 2 N algorithm, is used for the computation of the state equations of linear system, in which the time step is adivided into 2 N precision step, then the matrix exponential function is calculated in the precision steps by using it′s Taylor series. Compared with Runge kutta method, the new method has the advantages of both analytics and numerical method, high precision and good stability. Therefore the large time step can be used to improve the calculation efficiency.