摘要
格莱姆矩阵是反映线性系统结构特性的重要指标,通过对时不变系统状态方程的分析,将指数矩阵精细积分法的关键思想,即加法定理和增量存储直接应用于格莱姆矩阵的求解,给出了格莱姆矩阵的具体计算方法,得到了其精确数值解.该求解方法不需要矩阵求逆运算,当系统矩阵奇异或不稳定时,均能高精度求解.最后通过两个数值算例的仿真,验证了以上方法的正确性和有效性.
The Gram Matrix is an important index for reflecting the structure characteristics of a linear time-invariant system.By analyzing the state equations for the linear time-variant system,the key idea of precise integration method（PIM）,namely the addition theorem and incremental storage technology,is applied to solve the Gram Matrix.The specific calculation method is given and the exact solution is also obtained.The matrix inversion is not required,even when the system is singular or unstable,it can also be solved with high precision.Finally,two numerical examples are given to demonstrate the correctness and validity of the method.
出处
《西安电子科技大学学报》
EI
CAS
CSCD
北大核心
2014年第6期106-110,共5页
Journal of Xidian University
基金
国家自然科学基金资助项目(51305321
51175398
51035006
51105290)
中央高校基本科研业务费专项资金资助项目(K5051304021)
