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1.
研究状态矩阵和控制输入矩阵均具不确定性广义周期时变系统的鲁棒H_∞控制问题.提出参数不确定性广义周期时变系统广义可镇定和广义二次可镇定且具有H_∞性能指标的概念,利用线性矩阵不等式(LMI)方法,得到了参数不确定性广义周期时变系统广义二次可镇定且具有H_∞性能指标γ的充要条件,给出了相应的鲁棒H_∞状态反馈控制律的设计方法.最后,通过数值算例说明了设计方法的有效性. 相似文献
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In this article, we present a weaker version of the class of generalized positive subdefinite matrices introduced by Crouzeix and Komlósi [J.P. Crouzeix and S. Komlósi, The Linear Complementarity Problem and the Class of Generalized Positive Subdefinite Matrices, Applied Optimization, Vol. 59, Kluwer, Dordrecht, 2001, pp. 45–63], which is new in the literature, and obtain some properties of weak generalized positive subdefinite (WGPSBD) matrices. We show that this weaker class of matrices is also captured by row-sufficient matrices introduced by Cottle et al. [R.W. Cottle, J.S. Pang, and V. Venkateswaran, Sufficient matrices and the linear complementarity problem, Linear Algebra Appl. 114/115 (1989), pp. 231–249] and show that for WGPSBD matrices under appropriate assumptions, the solution set of a linear complementarity problem is the same as the set of Karush–Kuhn–Tucker-stationary points of the corresponding quadratic programming problem. This further extends the results obtained in an earlier paper by Neogy and Das [S.K. Neogy and A.K. Das, Some properties of generalized positive subdenite matrices, SIAM J. Matrix Anal. Appl. 27 (2006), pp. 988–995]. 相似文献
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A solution of the affine quadratic inverse eigenvalue problem 总被引:1,自引:0,他引:1
The quadratic inverse eigenvalue problem (QIEP) is to find the three matrices M,C, and K, given a set of numbers, closed under complex conjugations, such that these numbers become the eigenvalues of the quadratic pencil P(λ)=λ2M+λC+K. The affine inverse quadratic eigenvalue problem (AQIEP) is the QIEP with an additional constraint that the coefficient matrices belong to an affine family, that is, these matrices are linear combinations of substructured matrices. An affine family of matrices very often arise in vibration engineering modeling and analysis. Research on QIEP and AQIEP are still at developing stage. In this paper, we propose three methods and the associated mathematical theories for solving AQIEP: A Newton method, an alternating projections method, and a hybrid method combining the two. Validity of these methods are illustrated with results on numerical experiments on a spring-mass problem and comparisons are made with these three methods amongst themselves and with another Newton method developed by Elhay and Ram (2002) [12]. The results of our experiments show that the hybrid method takes much smaller number of iterations and converges faster than any of these methods. 相似文献
5.
W.Y Tan 《Journal of multivariate analysis》1979,9(3):452-459
This paper investigates the estimation of covariance matrices in multivariate mixed models. Some sufficient conditions are derived for a multivariate quadratic form and a linear combination of multivariate quadratic forms to be the BQUE (quadratic unbiased and severally minimum varianced) estimators of its expectations. 相似文献
6.
本文研究了一类具有特殊结构的无限维二次型, 得到这类二次型的对称矩阵是符号为多项式的模的平方的Laurent 矩阵, 进一步得到了这类二次型是强正定的判断标准以及一类Weyl-Heisenberg 框架的构造. 本文还研究了这类二次型的矩阵的所有有限维主对角子矩阵的强正定性, 并由此得到一类子空间Weyl-Heisenberg 框架的构造. 最后举例说明本文的主要结果及其应用. 本文建立了两个看似不相关的领域间的联系. 相似文献
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Solving Standard Quadratic Optimization Problems via Linear, Semidefinite and Copositive Programming 总被引:2,自引:2,他引:0
The problem of minimizing a (non-convex) quadratic function over the simplex (the standard quadratic optimization problem) has an exact convex reformulation as a copositive programming problem. In this paper we show how to approximate the optimal solution by approximating the cone of copositive matrices via systems of linear inequalities, and, more refined, linear matrix inequalities (LMI's). In particular, we show that our approach leads to a polynomial-time approximation scheme for the standard quadratic optimzation problem. This is an improvement on the previous complexity result by Nesterov who showed that a 2/3-approximation is always possible. Numerical examples from various applications are provided to illustrate our approach. 相似文献
9.
We study matrices over general rings which are sums of nilpotent matrices. We show that over commutative rings all matrices with nilpotent trace are sums of three nilpotent matrices. We characterize 2-by-2 matrices with integer entries which are sums of two nilpotents via the solvability of a quadratic Diophantine equation. Some exemples in the case of matrices over noncommutative rings are given. 相似文献
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Geometry of 2×2 hermitian matrices 总被引:2,自引:0,他引:2
Let D be a division ring which possesses an involution a→ā. Assume that F = {a∈D|a=ā} is a proper subfield of D and is contained in the center of D. It is pointed out that if D is of characteristic not two, D is either a separable quadratic extension of F or a division ring of generalized quaternions over F and that if D is of characteristic two, D is a separable quadratic extension of F. Thus the trace map Tr: D→F,hermitian matrices over D when n≥3 and now can be deleted. When D is a field, the fundamental theorem of 2×2 hermitian matrices over D has already been proved. This paper proves the fundamental theorem of 2×2 hermitian matrices over any division ring of generalized quaternions of characteristic not two. 相似文献
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LetD be a division ring which possesses an involution a → α . Assume that
is a proper subfield ofD and is contained in the center ofD. It is pointed out that ifD is of characteristic not two, D is either a separable quadratic extension of F or a division ring of generalized quaternions
over F and that if D is of characteristic two,D is a separable quadratic extension ofF. Thus the trace map Tr:D → F, a → a + a is always surjective, which is formerly posed as an assumption in the fundamental theorem of n×n hermitian
matrices overD when n ≥ 3 and now can be deleted. WhenD is a field, the fundamental theorem of 2 × 2 hermitian matrices overD has already been proved. This paper proves the fundamental theorem of 2×2 hermitian matrices over any division ring of generalized
quaternions of characteristic not two
This research was completed during a visit to the Academy of Mathematics and System Sciences, Chinese Academy of Sciences. 相似文献
13.
William C. Waterhouse 《Linear and Multilinear Algebra》1985,17(2):101-106
We show that over any cummutative ring R,the combinations, of 2 × 2 minors are the only quadratic forms vanishing on the matrices of rank 1. Hence any invertible linear transformation on matrices that preserves the rank-1 set over R will automatically do the same over all extensions of R. Similarly, the linear combinations of 4 × 4 Paffians are the only quadratic forms vanishing on the alternating matrices of rank 2. Hence again any invertible transformation preserving that set over R will do so formally. This fact allows us to determine the collection of such transformations 相似文献
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Olga Taussky 《Linear and Multilinear Algebra》1981,10(4):309-318
A treatment by integral matrices is given for composition of pairs of integral quadratic forms with the same discriminant. The forms are associated with a pair of similar 2 × 2 matrices AB with irrational eigen values which generate the maximal order. The most general integral similarity between AB is given by a matrix whose entries are linear forms in two indeterminates with integral coefficients. This matrix is a "compositum" of two factors of the same nature. By equating determinants a composition of two quadratic forms results. The method can be generalized to n × n matrices. 相似文献
15.
In this note, we discuss some properties of a quadratic formulation for linear complementarity problems. Projected SOR methods proposed by Mangasarian apply to symmetric matrices only. The quadratic formulation discussed here makes it possible to use these SOR methods for solving nonsymmetric LCPs. SOR schemes based on this formulation preserve sparsity. For proper choice of a free parameter, this quadratic formulation also preserves convexity. The value of the quadratic function for the solution of original LCP is also known. 相似文献
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Within the framework of the multiple Nevanlinna–Pick matrix interpolation and its related matrix moment problem, we study the rank of block moment matrices of various kinds, generalized block Pick matrices and generalized block Loewner matrices, as well as their Potapov modifications, generated by Nevanlinna matrix functions, and derive statements either on rank (or inertia) invariance in different senses or on rank variation of such types of block matrices (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
17.
Yongge Tian 《Linear and Multilinear Algebra》2013,61(11):1237-1246
A square matrix A of order n is said to be tripotent if A 3?=?A. In this note, we give a nine-term disjoint idempotent decomposition for the linear combination of two commutative tripotent matrices and their products. Using the decomposition, we derive some closed-form formulae for the eigenvalues, determinant, rank, trace, power, inverse and group inverse of the linear combinations. In particular, we show that the linear combinations of two commutative tripotent elements and their products can produce 39?=?19,683 tripotent elements. 相似文献
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王顺绪 《高等学校计算数学学报》2010,32(2)
<正>1引言陀螺系统特征值问题是转子动力学中的基本问题,是一类特殊的二次特征值问题.假设M和K是n阶对称矩阵,C是n阶反对称矩阵,则二次特征值问题(λ~2M+λC+K)x=0(1) 相似文献
19.
Spectral estimates for unreduced symmetric KKT systems arising from Interior Point methods 下载免费PDF全文
Benedetta Morini Valeria Simoncini Mattia Tani 《Numerical Linear Algebra with Applications》2016,23(5):776-800
We consider symmetrized Karush–Kuhn–Tucker systems arising in the solution of convex quadratic programming problems in standard form by Interior Point methods. Their coefficient matrices usually have 3 × 3 block structure, and under suitable conditions on both the quadratic programming problem and the solution, they are nonsingular in the limit. We present new spectral estimates for these matrices: the new bounds are established for the unpreconditioned matrices and for the matrices preconditioned by symmetric positive definite augmented preconditioners. Some of the obtained results complete the analysis recently given by Greif, Moulding, and Orban in [SIAM J. Optim., 24 (2014), pp. 49‐83]. The sharpness of the new estimates is illustrated by numerical experiments. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
20.
M. Minoux 《European Journal of Operational Research》1984,18(3):377-387
Network flow problems with quadratic separable costs appear in a number of important applications such as; approximating input-output matrices in economy; projecting and forecasting traffic matrices in telecommunication networks; solving nondifferentiable cost flow problems by subgradient algorithms. It is shown that the scaling technique introduced by Edmonds and Karp (1972) in the case of linear cost flows for deriving a polynomial complexity bound for the out-of-kilter method, may be extended to quadratic cost flows and leads to a polynomial algorithm for this class of problems. The method may be applied to the solution of singly constrained quadratic programs and thus provides an alternative approach to the polynomial algorithm suggested by Helgason, Kennington and Lall (1980). 相似文献