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Linear Differential Inequalities
SIAM Journal on Mathematical Analysis, 1978A notion of generalized zero with respect to a linear differential operator $L_n $ for a function f at a singular point of the operator was introduced by Levin and further considered by Willett. This involved a comparison of f with certain solutions of $L_n y = 0$ near the singular point. It is shown that the role of these solutions may be fulfilled by
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Solution of Linear Inequalities
IEEE Transactions on Computers, 1970A method for solving systems of linear inequalities, consistent and inconsistent, corresponding to the separable and nonseparable cases in pattern recognition is presented. Attempts are made to evaluate the speed and efficiency of the algorithm.
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Linear Inequality Scaling Problems
SIAM Journal on Optimization, 1992The author shows that the linear inequality scaling problems (LISP) is a generalization of the linear equality scaling problem and that it unifies a number of matrix-scaling problems that have been studied recently. Further, it is shown that LISP can be reduced to one of two convex optimization problems and these reductions are used to characterize ...
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Linear Equations and Linear Inequalities
2002While Chapter 1 reviews general structural aspects of real vector spaces, we now discuss fundamental computational techniques for linear systems in this chapter. For convenience of the discussion, we generally assume that the coefficients of the linear systems are real numbers.
Ulrich Faigle, Walter Kern, Georg Still
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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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Linear Inequalities Over Complex Cones
Canadian Mathematical Bulletin, 1973The basic solvability theorems of Farkas [2] and Levinson [4] were recently extended in different directions by Ben-Israel [1] and Kaul [3].The theorem stated in this note generalizes both results of Ben-Israel and Kaul and is applicable to nonlinear programming over complex cones.
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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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Linear inequalities for covering codes. II. Triple covering inequalities
IEEE Transactions on Information Theory, 1992Summary: The linear inequality method for covering codes is generalized. This method reduces the study of covering codes to the study of some local covering problems. One of these problems, the so-called 1-3 covering system, is formulated and studied in detail.
Zhang, Zhen, Lo, Chiaming
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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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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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