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Convex Matrix Inequalities Versus Linear Matrix Inequalities
IEEE Transactions on Automatic Control, 2009Most linear control problems lead directly to matrix inequalities (MIs). Many of these are badly behaved but a classical core of problems are expressible as linear matrix inequalities (LMIs). In many engineering systems problems convexity has all of the advantages of a LMI. Since LMIs have a structure which is seemingly much more rigid than convex MIs,
J.W. Helton +3 more
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Positivity and Linear Matrix Inequalities
European Journal of Control, 2002zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Genin, Y. +5 more
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On linearized versions of matrix inequalities
Linear Algebra and its Applications, 2023The authors prove linearized versions of the Aleksandrov-Fenchel and Brunn-Minkowski inequalities for positive semidefinite matrices. In order to present the results some definitions are needed. Given \(n\ge 1\) and arbitrary \(n\times n\) matrices \(A_1,\cdots,A_n\), denote by \(A_j^{(i)}\) the \(i\)-th column of the matrix \(A_j\).
de Vries, Christopher +2 more
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Optimal linear-quadratic control: From matrix equations to linear matrix inequalities
Automation and Remote Control, 2011zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Balandin, D. V., Kogan, M. M.
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Linear Matrix Inequalities in Control Problems
Differential Equations, 2020zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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