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Matrix Function (matrix + function)

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Mathematics and Statistics50%
Engineering50%

Selected Abstracts

Boundary value problems with eigenvalue depending boundary conditions

MATHEMATISCHE NACHRICHTEN, Issue 5 2009
Jussi Behrndt
Abstract We investigate some classes of eigenvalue dependent boundary value problems of the form where A , A+ is a symmetric operator or relation in a Krein space K, , is a matrix function and ,0, ,1 are abstract boundary mappings. It is assumed that A admits a self-adjoint extension in K which locally has the same spectral properties as a definitizable relation, and that , is a matrix function which locally can be represented with the resolvent of a self-adjoint definitizable relation. The strict part of , is realized as the Weyl function of a symmetric operator T in a Krein space H, a self-adjoint extension à of A × T in K × H with the property that the compressed resolvent PK (à , ,),1|Kk yields the unique solution of the boundary value problem is constructed, and the local spectral properties of this so-called linearization à are studied. The general results are applied to indefinite Sturm,Liouville operators with eigenvalue dependent boundary conditions (© 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]

Stability analysis for discrete-time fuzzy system by utilizing homogeneous polynomial matrix function,

ASIAN JOURNAL OF CONTROL, Issue 6 2009
Likui Wang
Abstract The purpose of this paper is to investigate the stability of nonlinear systems represented by a Takagi-Sugeno discrete-time fuzzy model. The homogeneous polynomial matrix function (HPMF) is developed to obtain new stabilization conditions. Applying the HPMF to the non-parallel distributed compensation (non-PDC) law and non-quadratic Lyapunov function, some new stabilization conditions are obtained by the following two means: (a) utilizing the popular idea of introducing additional variables for some fixed degree of the HPMF; and (b) increasing the degree of the HPMF. It is shown that the conditions obtained with approach (a) are less conservative than some sufficient stability conditions available in the literature to date. It is also shown that as the degree of HPMF increases the conditions obtained under (b) become less conservative. An example is provided to illustrate how the proposed approaches compare with other techniques available in the literature. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society [source]

Quantitative methods in nonlinear dynamics: novel approaches to liapunov's matrix functions, A. A. Martynyuk, Marcel Dekker, New York, 2002, 301 pp., Price $159.95, ISBN 0824707354

INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 9 2006
Zoran Gajic
No abstract is available for this article. [source]

Generalized factorization for N×N Daniele,Khrapkov matrix functions

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 13 2001
M. C. Câmara
Abstract A generalization to N×N of the 2×2 Daniele,Khrapkov class of matrix-valued functions is proposed. This class retains some of the features of the 2×2 Daniele,Khrapkov class, in particular, the presence of certain square-root functions in its definition. Functions of this class appear in the study of finite-dimensional integrable systems. The paper concentrates on giving the main properties of the class, using them to outline a method for the study of the Wiener,Hopf factorization of the symbols of this class. This is done through examples that are completely worked out. One of these examples corresponds to a particular case of the motion of a symmetric rigid body with a fixed point (Lagrange top). Copyright © 2001 John Wiley & Sons, Ltd. [source]