Results 241 to 250 of about 238,956 (287)

On linearized versions of matrix inequalities

Linear Algebra and its Applications, 2023
The 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, Lombardi, Nico, Saorín Gómez, Eugenia   +2 more
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Optimal linear-quadratic control: From matrix equations to linear matrix inequalities

Automation and Remote Control, 2011
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Balandin, D. V., Kogan, M. M.
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Linear Matrix Inequalities in Control Problems

Differential Equations, 2020
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Linear Matrix Inequalities in Control

2007
This 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, Turner, MC, Postlethwaite, I   +2 more
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Differential Linear Matrix Inequalities Optimization

IEEE Control Systems Letters, 2019
This letter proposes a new method to solve convex programming problems with constraints expressed by differential linear matrix inequalities (DLMIs). Initially, feasible solutions of interest are characterized and a general numerical method, based on the well known outer linearization technique, is proposed and discussed from theoretical and numerical ...
Tiago R. Goncalves, Gabriela W. Gabriel, Jose C. Geromel   +2 more
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Linear Matrix Inequalities in Control Systems with Uncertainty

Automation and Remote Control, 2021
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Polyak, B. T., Khlebnikov, M. V., Shcherbakov, P. S.   +2 more
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Dilated Linear Matrix Inequalities

2017
The history of the use of linear matrix inequalities (LMIs) in the context of systems and control dates back more than 120 years. This story probably began in about 1890, when Aleksandr Mikhailovich Lyapunov published his fundamental work on the stability of motion.
Yagoubi, Mohamed, Feng, Yu
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Error Bounds for Linear Matrix Inequalities

SIAM Journal on Optimization, 2000
Summary: For iterative sequences that converge to the solution set of a linear matrix inequality, we show that the distance of the iterates to the solution set is at most \( O(\varepsilon^{2^{-d}})\). The nonnegative integer \(d\) is the so-called degree of singularity of the linear matrix inequality, and \(\varepsilon \) denotes the amount of ...
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Fuzzy Dual Linear Matrix Inequalities

2017
LMI formalism has received an increasing acceptance for the formulation of feasible sets with crisp optimization problems. The new concepts proposed in this chapter are applied to the representation of fuzzy LMI domains using the introduced semi positive definiteness of fuzzy dual matrices.
Mora-Camino, Felix, Nunes Cosenza, Carlos Alberto   +1 more
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Linear Matrix Inequalities

2011
The origin of Linear Matrix Inequalities (LMIs) goes back as far as 1890, although they were not called this way at that time, when Lyapunov showed that the stability of a linear system \( {\bf {\dot x}} = {\bf {Ax}} \) is equivalent to the existence of a positive definite matrix P, which satisfies the matrix inequality\( \bf {{A^T}P} + \bf {PA} < \bf {
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