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Error Bounds for Linear Matrix Inequalities
SIAM Journal on Optimization, 2000Summary: 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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Linear Matrix Inequalities in Control Problems
Differential Equations, 2020zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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The projective method for solving linear matrix inequalities
Mathematical Programming, 1997Numerous problems in control and systems theory can be formulated in terms of linear matrix inequalities (LMI). Since solving an LMI amounts to a convex optimization problem, such formulations are known to be numerically tractable. However, the interest in LMI-based design techniques has really surged with the introduction of efficient interior-point ...
Pascal Gahinet, Arkadi Nemirovski
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Grasp analysis as linear matrix inequality problems
Proceedings 1999 IEEE International Conference on Robotics and Automation (Cat. No.99CH36288C), 2000Three fundamental problems in the study of grasping and dextrous manipulation with multifingered robotic hands are as follows, a) Given a robotic hand and a grasp characterized by a set of contact points and the associated contact models, determine if the grasp has force closure, b) Given a grasp along with robotic hand kinematic structure and joint ...
Han, Li +2 more
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Dilated Linear Matrix Inequalities
2017The 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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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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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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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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The D-decomposition technique for linear matrix inequalities
Automation and Remote Control, 2006zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Polyak, B. T., Shcherbakov, P. S.
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On the Low Rank Solutions for Linear Matrix Inequalities
Mathematics of Operations Research, 2008In this paper we present a polynomial-time procedure to find a low-rank solution for a system of linear matrix inequalities (LMI). The existence of such a low-rank solution was shown in the work of Au-Yeung and Poon and the work of Barvinok. In the approach of Au-Yeung and Poon an earlier unpublished manuscript of Bohnenblust played an essential role.
Wenbao Ai, Yongwei Huang, Shuzhong Zhang
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A neural network for linear matrix inequality problems
IEEE Transactions on Neural Networks, 2000Gradient-type Hopfield networks have been widely used in optimization problems solving. This paper presents a novel application by developing a matrix oriented gradient approach to solve a class of linear matrix inequalities (LMIs), which are commonly encountered in the robust control system analysis and design.
Chun-Liang Lin +2 more
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