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Bilateral Polynomial Equations With Unimodular Right-Hand-Side Matrices

Kaczorek T.

International Journal of Applied Mathematics and Computer Science

2003

Vol. 13, no 4

511-514

Necessary and sufficient conditions are established for the existence of a solution to some bilateral polynomial matrix equations with unimodular right-hand-side matrices. A procedure for the computation of the solution is derived and illustrated by a numerical example. Two examples of applications of bilateral polynomial matrix equations are presented.

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.