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Independence of asymptotic stability of positive 2D linear systems with delays of their delays

Tadeusz Kaczorek (2009)

International Journal of Applied Mathematics and Computer Science

It is shown that the asymptotic stability of positive 2D linear systems with delays is independent of the number and values of the delays and it depends only on the sum of the system matrices, and that the checking of the asymptotic stability of positive 2D linear systems with delays can be reduced to testing that of the corresponding positive 1D systems without delays. The effectiveness of the proposed approaches is demonstrated on numerical examples.

Inertias and ranks of some Hermitian matrix functions with applications

Xiang Zhang, Qing-Wen Wang, Xin Liu (2012)

Open Mathematics

Let S be a given set consisting of some Hermitian matrices with the same size. We say that a matrix A ∈ S is maximal if A − W is positive semidefinite for every matrix W ∈ S. In this paper, we consider the maximal and minimal inertias and ranks of the Hermitian matrix function f(X,Y) = P − QXQ* − TYT*, where * means the conjugate and transpose of a matrix, P = P*, Q, T are known matrices and for X and Y Hermitian solutions to the consistent matrix equations AX =B and YC = D respectively. As applications,...

Inverse eigenvalue problem of cell matrices

Sreyaun Khim, Kijti Rodtes (2019)

Czechoslovak Mathematical Journal

We consider the problem of reconstructing an n × n cell matrix D ( x → ) constructed from a vector x → = ( x 1 , x 2 , ⋯ , x n ) of positive real numbers, from a given set of spectral data. In addition, we show that the spectra of cell matrices D ( x → ) and D ( π ( x → ) ) are the same for every permutation π ∈ S n .

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