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A bisection method for computing the H_infinity-norm of a transfer matrix and related problems
Transfer matrix singular value assessment the Hamiltonian matrix characteristic values of linear algebra
2015/8/13
Inspired by recent work of Byers we establish a simple connection between the singular values of a transfer matrix evaluated along the imaginary axis and the imaginary eigenvalues of a related Hamilto...
Linear matrix inequalities in system and control theory
Linear matrix inequality system the control theory and linear matrix inequality affine combination symmetric positive semidefinite matrix
2015/8/12
A wide variety of problems in system and control theory can be formulated (or reformulated) as convex optimization problems involving linear matrix inequalities, that is, constraints requiring an affi...
Control systems analysis and synthesis via linear matrix inequalities
Control theory and linear matrix inequality the numerical algebraic riccati inequality lyapunov
2015/8/12
A wide variety of problems in systems and control theory can be cast or recast as convex problems that involve linear matrix inequalities (LMIs). For a few very special cases there are “analytical sol...
History of linear matrix inequalities in control theory
Linear matrix inequality control control theory tool control applications
2015/8/12
The purpose of this paper is to give a historical view of Linear Matrix Inequalities in control and system theory. Not surprisingly, it appears that LMIs have been involved in some of the major events...
Multiobjective H_2/H_infinity-optimal control via finite dimensional Q-parametrization and linear matrix inequalities
Controller design convex semidefinite programming impulse response
2015/8/11
The problem of multi-objective H2/H-infinity optimal controller design is reviewed. There is as yet no exact solution to this problem. We present a method based on that proposed by Scherer. The proble...
Determinant maximization with linear matrix inequality constraints
Matrix linear matrix inequality (lmi) computational geometry statistics system identification communication theory
2015/8/11
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 desig...
Least-squares covariance matrix adjustment
Symmetric matrices linear equations inequalities the original matrix
2015/8/10
We consider the problem of finding the smallest adjustment to a given symmetric n by n matrix, as measured by the Euclidean or Frobenius norm, so that it satisfies some given linear equalities and ine...
A class of asynchronous matrix multi-splitting multi-parameter
relaxation methods, including the asynchronous matrix multisplitting
SAOR, SSOR and SGS methods as well as the known asynchronous matri...
New estimates are provided for singular values of a matrix in this paper. These results generalize and improve corresponding estimates for singular values in [4]-[6].
By making use of the quotient singular value decomposition (QSVD) of a matrix pair, this paper establishes the necessary and sufficient conditions for the existence of and the expressions for the gene...
Triangular Matrix Representations of Rings of Generalized Power Series
Generalized triangular matrix representation Twisted generalized power series ring PWP ring Triangulating dimension
2007/12/12
Let $R$ be a ring and $S$ a cancellative and torsion-free monoid and $\leq$ a strict order on $S$. If either $(S, \leq)$ satisfies the condition that $0\leq s$ for all $s\in S$, or $R$ is reduced, the...
In this paper, the unitarily invariant norm $\|\cdot\|$ on $\BC^{m\times
n}$ is used. We first discuss the problem under what case, a
rectangular matrix $A$ has minimum condition number $K (A)=\| A ...
MATRIX ANALYSIS TO ADDITIVE SCHWARZ METHODS
2007/12/11
Matrix analysis on additive Schwarz methods as preconditioners is given
in this paper. Both cases of with and without coarse mesh are
considered. It is pointed out that an advantage of matrix analys...
A preconditioning method for the finite element stiffness matrix is given in this paper. The triangulation is refined in a subregion; the preconditioning process is composed of resolution of two regul...
On the Block Independence in $G$-Inverse and Reflexive Inner Inverse of A Partitioned Matrix
$G$-inverse reflexive inner inverse partitioned matrices block independence QQQQQ-SVD
2007/12/11
By applying the multiple quotient singular value decomposition QQQQQ-SVD, we study the block independence in $g$-inverse and reflexive inner inverse of $2\times 2$ partitioned matrices, and prove a co...