时不变系统格莱姆矩阵的精细积分

doi:10.3969/j.issn.1001-2400.2014.06.018

J4 ›› 2014, Vol. 41 ›› Issue (6): 106-110.doi: 10.3969/j.issn.1001-2400.2014.06.018

• Original Articles • Previous Articles Next Articles

Precise integration method for the Gram matrix of time-invariant systems

LI Sulan¹;REN Yuanhao¹;BAO Hong¹;ZHANG Wei²

(1. Ministry of Education Key Lab. of Electronic Equipment Structure Design, Xidian Univ., Xi'an 710071, China;
2. Wuhan Second Ship Design and Research Institute, Wuhan 430064, China)

Received:2013-07-18 Online:2014-12-20 Published:2015-01-19
Contact: LI Sulan E-mail:slli@xidian.edu.cn
About author:李素兰(1982-)，女，讲师，西安电子科技大学博士研究生，E-mail：slli@xidian.edu.cn．

Abstract

Abstract:

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.

Key words: Gram matrix, precise integration method, numerical method

CLC Number:

O241.4

LI Sulan;REN Yuanhao;BAO Hong;ZHANG Wei. Precise integration method for the Gram matrix of time-invariant systems[J].J4, 2014, 41(6): 106-110.

References

Gram matrix|precise integration method|numerical method
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Precise integration method for the Gram matrix of time-invariant systems

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