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In convex optimization, a linear matrix inequality (LMI) is an expression of the form ():= + + + + where = [, =, …,] is a real vector,,,, …, are symmetric matrices, is a generalized inequality meaning is a positive semidefinite matrix belonging to the positive semidefinite cone + in the subspace of symmetric matrices .
Finsler's lemma can be used to give novel linear matrix inequality (LMI) characterizations to stability and control problems. [4] The set of LMIs stemmed from this procedure yields less conservative results when applied to control problems where the system matrices has dependence on a parameter, such as robust control problems and control of ...
In mathematics, there are many kinds of inequalities involving matrices and linear operators on Hilbert spaces. This article covers some important operator inequalities connected with traces of matrices. [1] [2] [3] [4]
Bennett's inequality, an upper bound on the probability that the sum of independent random variables deviates from its expected value by more than any specified amount Bhatia–Davis inequality , an upper bound on the variance of any bounded probability distribution
It establishes a relation between a linear matrix inequality involving the state space constructs A, B, C and a condition in the frequency domain. The Kalman–Popov–Yakubovich lemma which was first formulated and proved in 1962 by Vladimir Andreevich Yakubovich [ 1 ] where it was stated that for the strict frequency inequality.
According to Marcus's former doctoral student Robert Grone, Marcus did pioneering, fundamental research in "numerical ranges, matrix inequalities, linear preservers and multilinear algebra". [ 1 ] [ 10 ] Marcus was the author or co-author of more than 200 articles and problem solutions and more than 20 books.
A spectrahedron. In convex geometry, a spectrahedron is a shape that can be represented as a linear matrix inequality.Alternatively, the set of n × n positive semidefinite matrices forms a convex cone in R n × n, and a spectrahedron is a shape that can be formed by intersecting this cone with an affine subspace.
The set of solutions of a real linear inequality constitutes a half-space of the 'n'-dimensional real space, one of the two defined by the corresponding linear equation. The set of solutions of a system of linear inequalities corresponds to the intersection of the half-spaces defined by individual inequalities.
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