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

时不变系统格莱姆矩阵的精细积分

李素兰¹;任元昊¹;保宏¹;张伟²

(1. 西安电子科技大学电子装备结构设计教育部重点实验室，陕西西安 710071；
2. 武汉市第二船舶设计研究所，湖北武汉 430064)

收稿日期:2013-07-18 出版日期:2014-12-20 发布日期:2015-01-19
通讯作者: 李素兰
基金资助:
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)

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
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．

摘要/Abstract

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．

关键词: 格莱姆矩阵, 精细积分法, 数值计算方法

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

中图分类号:

O241.4

李素兰;任元昊;保宏;张伟. 时不变系统格莱姆矩阵的精细积分[J]. J4, 2014, 41(6): 106-110.

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.

参考文献

Gram matrix|precise integration method|numerical method
［1］ Chesi G. A Gram-SOS Approach for Robust Stability Analysis of Discrete Time Systems with Time Varying Uncertainty ［C］//American Control Conference. Piscataway: IEEE, 2013: 5863-5868.
［2］ Korres G N, Manousakis N M. Observability Analysis and Restoration for State Estimation Using SCADA and PMU Data ［C］//IEEE Power and Energy Society General Meeting. Washington: IEEE Computer Society, 2012: 1-8.
［3］ Ramona M, Richard G, David B. Multiclass Feature Selection with Kernel Gram Matrix Based Criteria ［J］. IEEE Transactions on Networks and Learning Systems, 2012, 23(10): 1611-1623.
［4］刘英, 赵维江, 龚书喜. 计算物理光学积分的几种数值方法的分析［J］. 西安电子科技大学学报, 2001, 28(4): 542-545.
Liu Ying, Zhao Weijiang, Gong Shuxi. An Analysis of Numerical Methods for Physical Optics Integral ［J］. Journal of Xidian University, 2001, 28(4): 542-545.
［5］宋巨龙, 徐晨. 一种新的积分算法［J］. 西安电子科技大学学报, 2004, 31(6): 967-970.
Song Julong, Xu Chen. A New Integration Method［J］. Journal of Xidian University, 2004, 31(6): 967-970.
［6］ Zhong Wanxie, Williams F W. A Precise Time Step Method ［J］. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 1994, 208(6): 427-430.
［7］ Lin J H, Shen W P, Williams F W. Accurate High Speed Computation of Nonstationary Random Seismic Response ［J］. Engineering Structures, 1997, 19(7): 586-593.
［8］谭述君, 钟万勰. 非齐次动力方程Duhamel项的精细积分［J］. 力学学报, 2007, 39(3): 374-381.
Tan Shujun, Zhong Wanxie. Precise Integration Method for Gram Terms Arising from Linear Systems ［J］. Chinese Journal of Theoretical and Applied Mechanics, 2007, 39(3): 374-381.

时不变系统格莱姆矩阵的精细积分

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

PDF (PC)

赞

可视化

被引次数

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 0

Metrics

本文评价

推荐阅读 0