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Positivity and Linear Matrix Inequalities
 EUR. J. CONTROL
, 2002
"... In this paper we first recall the general theory of Popov realizations of parahermitian transfer functions in the context of generalized state space systems. We then use this general framework to derive linear matrix inequalities for various problems in systems and control. Finally, we indicate h ..."
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Cited by 7 (3 self)
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In this paper we first recall the general theory of Popov realizations of parahermitian transfer functions in the context of generalized state space systems. We then use this general framework to derive linear matrix inequalities for various problems in systems and control. Finally, we indicate
Linear Matrix Inequality . . .
, 2002
"... This article concerns which subsets of R can be represented with Linear Matrix Inequalities, LMIs? This gives some perspective on the scope and limitations of one of the most powerful techniques commonly used in control theory. Also before having much hope of representing engineering problems as ..."
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This article concerns which subsets of R can be represented with Linear Matrix Inequalities, LMIs? This gives some perspective on the scope and limitations of one of the most powerful techniques commonly used in control theory. Also before having much hope of representing engineering problems
Contractors and Linear Matrix Inequalities
"... Abstract. Linear Matrix Inequalities (LMI for short) is a large class of convex constraints. Boxes, Ellipsoids, linear constraints, can be represented by LMIs. Intersection of LMIs are also LMIs. Interior point methods are able to minimize or maximize any linear criterion of LMIs with a complexity ..."
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Abstract. Linear Matrix Inequalities (LMI for short) is a large class of convex constraints. Boxes, Ellipsoids, linear constraints, can be represented by LMIs. Intersection of LMIs are also LMIs. Interior point methods are able to minimize or maximize any linear criterion of LMIs with a com
Infeasibility certificates for linear matrix inequalities
"... Abstract. Farkas ’ lemma is a fundamental result from linear programming providing linear certificates for infeasibility of systems of linear inequalities. In semidefinite programming, such linear certificates only exist for strongly infeasible linear matrix inequalities. We provide nonlinear algebr ..."
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Cited by 3 (1 self)
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Abstract. Farkas ’ lemma is a fundamental result from linear programming providing linear certificates for infeasibility of systems of linear inequalities. In semidefinite programming, such linear certificates only exist for strongly infeasible linear matrix inequalities. We provide nonlinear
DETERMINANT MAXIMIZATION WITH LINEAR MATRIX INEQUALITY CONSTRAINTS
"... The problem of maximizing the determinant of a matrix subject to linear matrix inequalities arises in many fields, including computational geometry, statistics, system identification, experiment design, and information and communication theory. It can also be considered as a generalization of the s ..."
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Cited by 229 (18 self)
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The problem of maximizing the determinant of a matrix subject to linear matrix inequalities arises in many fields, including computational geometry, statistics, system identification, experiment design, and information and communication theory. It can also be considered as a generalization
Error Bounds for Linear Matrix Inequalities
, 1998
"... 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(ffl 2 \Gammad ). The nonnegative integer d is the socalled degree of singularity of the linear matrix inequality, and ffl denotes th ..."
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Cited by 7 (0 self)
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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(ffl 2 \Gammad ). The nonnegative integer d is the socalled degree of singularity of the linear matrix inequality, and ffl denotes
Linear Matrix Inequalities.............
"... For contact information about worldwide offices, see the MathWorks Web site. ..."
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For contact information about worldwide offices, see the MathWorks Web site.
A Linear Matrix Inequality Approach to H∞ Control
 INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL
, 1994
"... The continuous and discretetime H∞ control problems are solved via elementary manipulations on linear matrix inequalities (LMI). Two interesting new features emerge through this approach: solvability conditions valid for both regular and singular problems, and an LMIbased parametrization of all H ..."
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Cited by 155 (11 self)
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The continuous and discretetime H∞ control problems are solved via elementary manipulations on linear matrix inequalities (LMI). Two interesting new features emerge through this approach: solvability conditions valid for both regular and singular problems, and an LMIbased parametrization of all
Exact algorithms for linear matrix inequalities
, 2015
"... Let A(x) = A0 + x1A1 + · · · + xnAn be a linear matrix, or pencil, generated by given symmetric matrices A0, A1,..., An of size m with rational entries. The set of real vectors x such that the pencil is positive semidefinite is a convex semialgebraic set called spectrahedron, described by a line ..."
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linear matrix inequality (LMI). We design an exact algorithm that, up to genericity assumptions on the input matrices, computes an exact algebraic representation of at least one point in the spectrahedron, or decides that it is empty. The algorithm does not assume the existence of an interior point
Results 1  10
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1,396,272