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Výpočet determinantu rozměrné matice Sylvesterova typu
Kujan, Petr ; Hromčík, M. ; Šebek, Michael
This work is devoted to computation of large n-D polynomial determinants with a special structure. Applications involve n-D systems theory (e.g. coprimeness test for two n-D polynomials) or the theory of algebraic equations. More specifically, these determinants were exploited by Chiasson recently to solve the practical problem of multilevel converter by a special computational procedure. To tackle the concerned problem it is essential to solve a system of polynomial equations with many unknowns.
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Numerical algorithms for polynomial matrices
Hromčík, Martin ; Šebek, Michael
This report is devoted to new numerical methods for computations with polynomials and polynomial matrices that are encountered when solving the problems of control systems design via the algebraic methods. A distinguishing feature ofour approach is the extensive employment of the discrete Fourier transform tech-niques, namely of the famous Fast Fourier Transform routine and its relation to polynomial interpolation and Z-transform.
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Polynomial matrices, LMIs and static output feedback
Henrion, Didier ; Kučera, V.
In the polynomial approach to systems control, the static output feedback problem can be formulated as follows: given two polynomial matrices D(s) and N(s), find a constant matrix K such that polynomial matrix D(s)+KN(s) is stable. In this paper, we show that solving this problem amounts to solving a linear matrix inequality with a non-convex rank constraint.
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