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An eigenvalue method for testing positive definiteness of a multivariate form

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成果类型:
期刊论文
作者:
Ni, Qin;Qi, Liqun;Wang, Fei
通讯作者:
Ni, Q.(niqfs@nuaa.edu.cn)
作者机构:
[Ni, Qin ] Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
[ Wang, Fei ] Department of Mathematics, Hunan City University, Yiyang, Hunan 413000, China
[ Qi, Liqun ] Department of Applied Mathematics, The Hong Kong Polytechnic University, Hong Kong, Hong Kong
通讯机构:
[Ni, Q] Nanjing Univ Aeronaut & Astronaut, Dept Math, Nanjing 210016, Peoples R China.
语种:
英文
关键词:
Eigenvalue method - Positive definiteness - Supersymmetric tensor - Symmetric hyperdeterminant
期刊:
Automatic Control, IEEE Transactions on
ISSN:
0018-9286
年:
2008
卷:
53
期:
5
页码:
1096-1107
文献类别:
WOS:Article;EI:Journal article (JA)
所属学科:
ESI学科类别:工程学;WOS学科类别:Automation & Control Systems;Engineering, Electrical & Electronic
入藏号:
WOS:000258868400001;EI:20083811573905
机构署名:
本校为其他机构
院系归属:
理学院
摘要:
In this paper, we present an eigenvalue method for testing positive definiteness of a multivariate form. This problem plays an important role in the stability study of nonlinear autonomous systems via Lyapunov's direct method in automatic control. At first we apply the D'Andrea-Dickenstein version of the classical Macaulay formulas of the resultant to compute the symmetric hyperdeterminant of an even order supersymmetric tensor. By using the supersymmetry property, we give detailed computation procedures for the Bezoutians and specified ordering of monomials in this approach. We then use these formulas to calculate the characteristic polynomial of a fourth order three dimensional supersymmetric tensor and give an eigenvalue method for testing positive definiteness of a quartic form of three variables. Some numerical results of this method are reported.
参考文献:
ANDERSON BD, 1974, IEEE T CIRCUITS SYST, VAS21, P300, DOI 10.1109/TCS.1974.1083834
Anderson B. D., 1975, IEEE T AUTOMAT CONTR, VAC20, P55
Becker E, 1996, PROG MATH, V143, P79
BJORCK A, 1970, MATH COMPUT, V24, P893, DOI 10.2307/2004623
BOSE NK, 1968, IEEE T AUTOMAT CONTR, VAC13, P447, DOI 10.1109/TAC.1968.1098953

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