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Banded matrix solvers and polynomial Diophantine equations
Hromčík, Martin ; Hurák, Zdeněk ; Frízel, R. ; Šebek, M.
Numerical procedures and codes for linear Diophantine polynomial equations are proposed in this paper based on the banded matrix algorithms and solvers. Both the scalar and matrix cases are covered. The algorithms and programs developed are based on the observation that a set of constant linear equations resulting from the polynomial problem features a special structure. This structure, known as Sylvester, or block Syelvester in the matrix case, can in turn be accommodated in the banded matrix framework.
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Modular shift of a polynomial matrix using Matlab
Hurák, Zdeněk ; Šebek, Michael
Efficient algorithm for modular shift of a polynomial matrix is proposed in this note.The algorithm avoids any iteration that is inherent in standard Euclidean algorithm for division of polynomial matrices.It assumes that the denominator polynomial matrix is row-reduced.If it is not,it can always be transformed into row-reduced form accepting some additional computational cost. Numerical experiments with an implementation of the proposed algorithm in Matlab are reported.
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Simultaneous feedback stabilization: A survey
Hurák, Zdeněk ; Šebek, Michael
This paper gives a short introduction into the topic of simultaneous feedback stabilization, which is recognized as one of the fundamental open problems in control theory. In this paper, some essential defnitions are given, the relation between strong and simultaneous stability is explained, the recent result on complexity of the topic is stated, and some recent approaches based on LMI paradigm are described. SISO systems are considered only.
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Návrh regulátoru pro VLT teleskop pomocí MATLABU
Hurák, Zdeněk ; Šebek, Michael
Článek ilustruje jednu iteraci procesu matlabského návrhu robustního regulátoru pro VLT teleskop (Very Large Telescope) provozovaný výzkumnou organizací ESO (European Southern Observatory) na observatoři v pohoří Paranal v Chile. Cílem návrhu je získat regulátor tlumící vliv větru a zároveň respektující přítomnost málo tlumených rezonančních módů v konstrukci teleskopu. Pro návrh byla vybrána metodika spoléhající na minimalizaci H nekonecno normy smíšené citlivostní funkce a použity funkce Polynom.Toolboxu.
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