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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,
Scott Mccullough +2 more
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Positivity and Linear Matrix Inequalities
European Journal of Control, 2002zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Nesterov Yurii +2 more
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SIAM Journal on Numerical Analysis, 1969
If y is perpendicular to xi, (I xixT)y = y, while (I xixT)xi = 0. Thus (I xix') projects an arbitrary vector y onto the hyperplane perpendicular to xi, and A corresponds to a sequence of projections. The matrix A arises in an algorithm which the author has studied [1], and Theorem 1 shows how the rate of convergence of this algorithm, for the case k ...
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If y is perpendicular to xi, (I xixT)y = y, while (I xixT)xi = 0. Thus (I xix') projects an arbitrary vector y onto the hyperplane perpendicular to xi, and A corresponds to a sequence of projections. The matrix A arises in an algorithm which the author has studied [1], and Theorem 1 shows how the rate of convergence of this algorithm, for the case k ...
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Eigenvalue Inequalities for Matrix Product
IEEE Transactions on Automatic Control, 2006We present a family of eigenvalue inequalities for the product of a Hermitian matrix and a positive-semidefinite matrix.
Fuzhen Zhang, Qingling Zhang 0001
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International Journal of Control, 1989
Abstract A new matrix inequality associated with bounds on solutions of algebraic Riccati and Lyapunov equations is presented. The improvement of the obtained result over the previously reported results is shown.
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Abstract A new matrix inequality associated with bounds on solutions of algebraic Riccati and Lyapunov equations is presented. The improvement of the obtained result over the previously reported results is shown.
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Solubility of matrix inequalities
Mathematical Notes of the Academy of Sciences of the USSR, 1984Translation from Mat. Zametki 36, No.5, 725-732 (Russian) (1984; Zbl 0565.15008).
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Matrix Mixed Mean Inequalities
Results in Mathematics, 2018zbMATH Open Web Interface contents unavailable due to conflicting licenses.
M. Alakhrass, M. Sababheh
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Inequalities for the trace of matrix product
IEEE Transactions on Automatic Control, 1994To obtain estimates of solutions of Lyapunov and Riccati equations which frequently occur in the stability analysis and optimal control design in linear control theory, many researchers have attempted to determine upper and lower bounds for the product of two matrices in terms of the trace of one matrix and the eigenvalues of the other.
Yuguang Fang +2 more
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Exact Algorithms for Linear Matrix Inequalities [PDF]
SIAM Journal on Optimization, 2016 Let $A(x)=A\_0+x\_1A\_1+...+x\_nA\_n$ be a linear matrix, or pencil, generated by given symmetric matrices $A\_0,A\_1,...,A\_n$ of size $m$ with rational entries. The set of real vectors x such that the pencil is positive semidefinite is a convex semi-algebraic set called spectrahedron, described by a linear matrix inequality (LMI).
Didier Henrion +2 more
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