A trace bound for a general square matrix product

Estimates of bounds on the solutions of Lyapunov and Riccati equations are important for analysis and synthesis of linear systems. In this paper, we propose new trace bounds for the product of two general matrices. The key point for removing the restriction of symmetry is to replace eigenvalues part...

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Bibliographic Details
Published inIEEE transactions on automatic control Vol. 45; no. 8; pp. 1563 - 1569
Main Authors Xing, Wei, Zhang, Qingling, Wang, Qiyi
Format Journal Article
LanguageEnglish
Published New York IEEE 01.08.2000
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects
Automation
Eigenvalues
Eigenvalues and eigenfunctions
Estimates
Linear matrix inequalities
Linear systems
Mathematical analysis
Matrices
Matrix decomposition
Mechanical engineering
Riccati equation
Riccati equations
Singular value decomposition
Symmetric matrices
Symmetry
Synthesis
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Summary:Estimates of bounds on the solutions of Lyapunov and Riccati equations are important for analysis and synthesis of linear systems. In this paper, we propose new trace bounds for the product of two general matrices. The key point for removing the restriction of symmetry is to replace eigenvalues partly by singular values in the equation of bounds. The results obtained are valid for both symmetric and nonsymmetric cases and give tighter bounds in certain cases.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0018-9286
1558-2523
DOI:10.1109/9.871773