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vol 63 / August, 2020
Article

DOI 10.17586/0021-3454-2019-62-9-791-797

UDC УДК 62.50

FORMATION OF CRITERION MATRICES OF MULTI-DIMENSIONAL DYNAMICAL SYSTEMS USING THE FADDEEV — LEVERRIER ALGORITHM

N. A. Vunder
ITMO University, Saint Petersburg, 197101, Russian Federation; postgraduete


N. A. Dudarenko
ITMO University, Saint Petersburg, 197101, Russian Federation; Associate professor


V. G. Melnikov
ITMO University, Saint Petersburg, 197101, Russian Federation; Professor


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Abstract. The problem of criterion matrices formation for the multidimensional dynamic systems is considered. The criterion matrices can be used for the properties analysis of a multidimensional system in a stationary state. The procedure of criterion matrices formation is considered in relation to the problem of estimating the tendency of multidimensional dynamic systems to degeneration, which is a measure of the robustness of a multidimensional system. The case of multidimensional continuous-time dynamic systems is considered as an example for criterion matrices construction. The problem is solved using the Faddeev — LeVerrier algorithm, which is supplemented by the Cayley — Hamilton theorem. The obtained real-valued construction for the formation of criterion matrices of the input-output relationship of multidimensional dynamical systems is focused on the problem of a priori express control of the degeneracy of dynamical systems of the multidimensional input — multidimensional output type in static.
Keywords: Faddeev — LeVerrier algorithm, condition number, degeneration, criterion matrix, Cayley — Hamilton theorem, degeneration factor

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