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Równania macierzowe I

Tomaszewski Witold

MINUT Matematyka i Informatyka na Uczelniach Technicznych

2020

Nr 2

29-40

Celem tego artykułu jest prezentacja metod rozwiązywania równań wielomianowych postaci f(X) = A, gdzie X jest niewiadomą macierzą, A macierzą kwadratową stopnia 2, a f(x) wielomianem o współczynnikach zespolonych.

The Relationship Between the Infinite Eigenvalue Assignment for Singular Systems and the Solvability of Polynomial Matrix Equations

Kaczorek T.

International Journal of Applied Mathematics and Computer Science

2003

Vol. 13, no 2

161-167

Two related problems, namely the problem of the infinite eigenvalue assignment and that of the solvability of polynomial matrix equations are considered. Necessary and sufficient conditions for the existence of solutions to both the problems are established. The relationships between the problems are discussed and some applications from the field of the perfect observer design for singular linear systems are presented.

Existence and Computation of the Set of Positive Solutions to Polynomial Matrix Equations

Kaczorek T., Łopatka R.

International Journal of Applied Mathematics and Computer Science

2000

Vol. 10, no 2

309-320

Necessary and sufficient conditions are established for the existence of positive solutions to polynomial diophatine equations. A method of computing of the set of positive solutions to a polynomial diophatine equation based on extreme points and extreme directions is proposed. The effectiveness of the method is demonstrated on a numerical example.

Positive solutions to polynomial matrix equations

Kaczorek T.

Applied Mathematics and Computer Science

1998

Vol. 8, no 2

403-415

Necessary and sufficient conditions are established for the existence of positive solutions to polynomial matrix equations. Two methods are proposed for determination of such solutions. As an example of applications it is shown that the determination of the transfer matrix of a positive controller for a closed-loop system with a given transfer matrix can be reduced to finding solutions to two suitable polynomial matrix equations.