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Linear Matrix Inequalities in Control
2007This chapter gives an introduction to the use of linear matrix inequalities (LMIs) in control. LMI problems are defined and tools described for transforming matrix inequality problems into a suitable LMI-format for solution. Several examples explain the use of these fundamental tools.
Herrmann, G +2 more
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Matrix Inequality Applications in Econometrics
2000Matrix inequalities play a large role in econometrics. Such inequalities essentially come in two kinds. One is concerned with inequalities of the scalar type involving scalar functions of matrices. A fine overview is offered by chapter 11 of the often-cited reference book of Magnus and Neudecker (1988).
Bekker, P.A., Wansbeek, T.J.
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A trace inequality for matrix product
IEEE Transactions on Automatic Control, 1995A well-known trace inequality for positive semidefinite matrices is extended to arbitrary Hermitian matrices. When using this result for the product of two matrices, when only one is Hermitian, the author improves a recent trace inequality by \textit{Y. Fang}, \textit{K. A. Loparo} and \textit{X. Fang} [ibid. 39, No. 12, 2489-2490 (1994; Zbl 0825.93107)
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A matrix-approach for proving inequalities
1989For special inequalities p ≤ q, where p, q are algebraic expressions such that for p and q corresponding matrices P, Q can be given, proofs can be performed by manipulating the rows of Q, such that the manipulation yields P. The paper gives an Ω with P=Ω(Q) where Ω can be seen as an algorithm in the classical sense because Ω=ω o ω o ...
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A Survey of Matrix Theory and Matrix Inequalities.
The American Mathematical Monthly, 1965A. S. H., Marvin Marcus, Henryk Minc
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Quadratic Matrix Inequalities with Applications to Data-Based Control
SIAM Journal on Control and Optimization, 2023Harry L Trentelman +2 more
exaly
Matrix inequality in distributional sense
1986zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Yao, Y. S., Lin, Ta-Feng
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