Isospectral Systems and its Application in Partial Pole Assignment Problem
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- 英文论文题名：Isospectral Systems and its Application in Partial Pole Assignment Problem
- 论文作者：Xiaobin Mao ; Weitai Liang
- 英文论文作者：Xiaobin Mao ; Weitai Liang ; Science and Technology on Information System Engineering Laboratory
- 年：2017
- 作者机构：Science and Technology on Information System Engineering Laboratory;
- 英文论文关键词：Isospectral Vibrating Systems ; Partial Pole Assignment ; Quadratic Pencils
- 会议召开时间：2017-07-26
- 会议录名称：第36届中国控制会议论文集（A）
- 英文会议录名称：Proceedings of the 36th Chinese Control Conference（A）
- 语种：英文
- 分类号：O241.8
- 学会代码：KZLL
- 会议名称：第36届中国控制会议
- 会议地点：中国辽宁大连
- 主办单位：中国自动化学会控制理论专业委员会
- 学会名称：中国自动化学会控制理论专业委员会
- 页数：5
- 文件大小：187k
- 原文格式：D
- 会议级别：全国
摘要
In this paper, we construct a class of isospectral vibrating systems from partial explicit spectrum and partial implicit spectrum. It extends the work of P. Lancaster in which the isospectral vibrating systems are constructed only from complete explicit data or complete implicit data. The result can be applied to solve the partial pole assignment problem for the secondorder system, such that the unwanted eigenvalues are moved to prescribed values and the wanted eigenvalues remain unchanged.Numerical example shows that the method is efficient.
In this paper, we construct a class of isospectral vibrating systems from partial explicit spectrum and partial implicit spectrum. It extends the work of P. Lancaster in which the isospectral vibrating systems are constructed only from complete explicit data or complete implicit data. The result can be applied to solve the partial pole assignment problem for the secondorder system, such that the unwanted eigenvalues are moved to prescribed values and the wanted eigenvalues remain unchanged.Numerical example shows that the method is efficient.
In this paper, we construct a class of isospectral vibrating systems from partial explicit spectrum and partial implicit spectrum. It extends the work of P. Lancaster in which the isospectral vibrating systems are constructed only from complete explicit data or complete implicit data. The result can be applied to solve the partial pole assignment problem for the secondorder system, such that the unwanted eigenvalues are moved to prescribed values and the wanted eigenvalues remain unchanged.Numerical example shows that the method is efficient.
引文
[1]Xiaowei Tang,Lihua Zhu,Vibration isolation and buffering design for equipment of vehicle-borne systems,Command information system and technology,2(4):68–70,2011.(in Chinese)
[2]Yingmin Li,Noise Analysis and noise reduction design for command and control system shelter,Command information system and technology,3(4):77–80,2012.(in Chinese)
[3]U.Prells and P.Lancaster,Isospectral vibrating systems.Part 2:Structure Preserving Transformations,Operator Theory:Advances and Applications,163:275–298,2005.
[4]B.N.Datta,S.Elhay,and Y.M.Ram,Orthogonality and partial pole assignment for the symmetric definite quadratic pencil,Linear Algebra and its Applications,257:29–48,1997.
[5]J.Qian and S.Xu,Robust partial eigenvalue assignment problem for the second-order system,Journal of sound and vibration,282:937–948,2005.
[6]Kuo Y C,Lin W W and Xu S F,Solutions of the Partially Described Inverse Quadratic Eigenvalue Problem,SIAM J Matrix Anal Appl,29(4):33–53,2006.
[7]I.Gohberg,P.Lancaster and L.Rodman.Matrix Polynomials.Academic Press,New York,1982.
[8]P.Lancaster,Isospectral vibrating systems.Part 1:The spectral method,Linear Algebra and its Applications,409:51–69,2005.
[9]I.Gohberg,P.Lancaster and L.Rodman.Matrices and Indefinite Scalar Products,Birkhauser,Basel,1983.
[10]Y.M.Ram and S.Elhay,Pole assignment in vibratory systems by multi-input control,Journal of Sound and Vibration,230:309–321,2000.
[11]D.J.Inman,Active modal control for smart structures,Philosophical Transactions of the Royal Society(special issue),359:205-219,2001.
[2]Yingmin Li,Noise Analysis and noise reduction design for command and control system shelter,Command information system and technology,3(4):77–80,2012.(in Chinese)
[3]U.Prells and P.Lancaster,Isospectral vibrating systems.Part 2:Structure Preserving Transformations,Operator Theory:Advances and Applications,163:275–298,2005.
[4]B.N.Datta,S.Elhay,and Y.M.Ram,Orthogonality and partial pole assignment for the symmetric definite quadratic pencil,Linear Algebra and its Applications,257:29–48,1997.
[5]J.Qian and S.Xu,Robust partial eigenvalue assignment problem for the second-order system,Journal of sound and vibration,282:937–948,2005.
[6]Kuo Y C,Lin W W and Xu S F,Solutions of the Partially Described Inverse Quadratic Eigenvalue Problem,SIAM J Matrix Anal Appl,29(4):33–53,2006.
[7]I.Gohberg,P.Lancaster and L.Rodman.Matrix Polynomials.Academic Press,New York,1982.
[8]P.Lancaster,Isospectral vibrating systems.Part 1:The spectral method,Linear Algebra and its Applications,409:51–69,2005.
[9]I.Gohberg,P.Lancaster and L.Rodman.Matrices and Indefinite Scalar Products,Birkhauser,Basel,1983.
[10]Y.M.Ram and S.Elhay,Pole assignment in vibratory systems by multi-input control,Journal of Sound and Vibration,230:309–321,2000.
[11]D.J.Inman,Active modal control for smart structures,Philosophical Transactions of the Royal Society(special issue),359:205-219,2001.