ISSN 0021-3454 (print version)
ISSN 2500-0381 (online version)
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vol 64 / March, 2021
Article

DOI 10.17586/0021-3454-2015-58-9-759-764

UDC 62.50

APPLICATION OF GRAM METHOD FOR RANGING OF PARAMETRIC UNCERTAINTIES

S. A. Alexandrova
Saint Petersburg National Research University of Information Technologies, Mechanics and Optics; student


O. V. Slita
Saint Petersburg National Research University of Information Technologies, Mechanics and Optics; Associate professor


A. V. Ushakov
ITMO University, Saint Petersburg, 197101, Russian Federation; Professor


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Abstract. The problem of output invariance of a closed-loop system with respect to uncertain parameters of the initial plant state matrix is considered. Two methods of uncertainties ranging by levels of influence on the closed-loop system output are proposed. The both methods use Gramians of the channels “control signal — plant output” and “parametric influence — plant output” controllability. An algorithm for parametric uncertainties ranging based on the methods is developed. An example demonstrating application of the methods is presented.
Keywords: parametric uncertainty, Gramian, ranging, singular values, generalized characteristic equation