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

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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.

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