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1
Content available remote Stability of Symmetrizable Interval Matrices
100%
Kowynia J.
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2000
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tom Vol. 48, nr 1
41-48
EN
Necessary and sufficient condition for stability of convex combination of symmetrizable matrices is given. Necessary and sufficient condition for stability of an interval matrix, symmetrizable by diagonal matrix is proposed.
2
Content available remote An algorithm for checking Hurwitz stability of K-symmetrizable interval matrices
80%
Kowynia J.
Control and Cybernetics
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2005
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tom Vol. 34, no 2
477-486
EN
The necessary and sufficient condition for stability of K-symmetrizable interval matrix is given. An algorithm for checking stability of K-symmetrizable interval matrix is proposed.
3
Content available remote Enclosures for the solution set of parametric interval linear systems
80%
Hladík M.
|
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nr 3
561-574
EN
We investigate parametric interval linear systems of equations. The main result is a generalization of the Bauer-Skeel and the Hansen-Bliek-Rohn bounds for this case, comparing and refinement of both. We show that the latter bounds are not provable better, and that they are also sometimes too pessimistic. The presented form of both methods is suitable for combining them into one to get a more efficient algorithm. Some numerical experiments are carried out to illustrate performances of the methods.
4
Content available remote Stability of an Interval Matrix Symmetrizable by Distinct Diagonal Matrices
80%
Kowynia J.
|
2001
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tom vol. 49, nr 3
433-443
EN
Stability of convex combination of matrices symmetrizable by diagonal matrices is considered. Necessary and sufficient condition for stability of some interval matrix, symmetrizable by distinct diagonal matrices is proposed.
5
Content available Intervals of certain classes of Z-matrices
70%
Kannan M. , Sivakumar K.
Discussiones Mathematicae - General Algebra and Applications
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2014
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tom 34
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nr 1
85-93
EN
Let A and B be M-matrices satisfying A ≤ B and J = [A,B] be the set of all matrices C such that A ≤ C ≤ B, where the order is component wise. It is rather well known that if A is an M-matrix and B is an invertible M-matrix and A ≤ B, then aA + bB is an invertible M-matrix for all a,b > 0. In this article, we present an elementary proof of a stronger version of this result and study corresponding results for certain other classes as well.
6
Content available Robust stability of a class of uncertain fractional order linear systems with pure delay
60%
Busłowicz M.
Archives of Control Sciences
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2015
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tom Vol. 25, no. 2
177--187
EN
The paper considers the robust stability problem of uncertain continuous-time fractional order linear systems with pure delay in the following two cases: a) the state matrix is a linear convex combination of two known constant matrices, b) the state matrix is an interval matrix. It is shown that the system is robustly stable if and only if all the eigenvalues of the state matrix multiplied by delay in power equal to fractional order are located in the open stability region in the complex plane. Parametric description of boundary of this region is derived. In the case a) the necessary and sufficient computational condition for robust stability is established. This condition is given in terms of eigenvalue-loci of the state matrix, fractional order and time delay. In the case b) the method for determining the rectangle with sides parallel to the axes of the complex plane in which all the eigenvalues of interval matrix are located is given and the sufficient condition for robust stability is proposed. This condition is satisfied if the rectangle multiplied by delay in power equal to fractional order lie in the stability region. The considerations are illustrated by numerical examples.
7
A note on eigenvalues of interval matrix
60%
Skrzypczyk J. , Witek H.
Zeszyty Naukowe Katedry Mechaniki Stosowanej / Politechnika Śląska
|
1999
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tom z. 10
273-278
EN
In the paper, we are concerned with interval - oriented methodology to model uncertainties of eigenvalues of an nxn interval real matrix. We investigate methods of calculation for characteristic polynomials of interval matrices. Presented methodology is probably the simplest way to model and to approximate vibration properties of systems with uncertain parameters.
PL
W pracy przedstawiono nowe pojęcia i wyniki dotyczące metodologii analizy zagadnień związanych z wartościami własnymi i wyznaczaniem współczynników wielomianu charakterystycznego macierzy rzeczywistych o współczynnikach interwałowych. Przedstawione ujęcie jest prawdopodobnie najprostszym sposobem aproksymacji w modelowaniu drgań i ich własności w systemach o parametrach niepewnych.
8
Content available Enclosures for the solution set of parametric interval linear systems
60%
Hladík M.
International Journal of Applied Mathematics and Computer Science
|
2012
|
tom Vol. 22, no. 3
561-574
EN
We investigate parametric interval linear systems of equations. The main result is a generalization of the Bauer-Skeel and the Hansen-Bliek-Rohn bounds for this case, comparing and refinement of both. We show that the latter bounds are not provable better, and that they are also sometimes too pessimistic. The presented form of both methods is suitable for combining them into one to get a more efficient algorithm. Some numerical experiments are carried out to illustrate performances of the methods.
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