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

DOI 10.17586/0021-3454-2017-60-9-826-833

UDC 62.50: 681.50.1

PECULIARITIES OF FREE-MOTION TRAJECTORIES OF CONTINUOUS SYSTEM IN THE FORM OF A SEQUENCE OF IDENTICAL OSCILLATORY UNITS

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


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


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Abstract. A stable continuous system with multiple complex conjugate eigenvalues of state matrix is considered. The system is realized as a consecutive chain of identical oscillatory links, so that the eigenvalue multiplicity is equal to half of state vector dimension. The case under investigation presuppose that the eigenvalues spectrum is represented by a modified Butterworth distribution and lies in a sector not wider than 60о. It is found that free motion norm of the system may demonstrate a considerable deviation from a monotonically decreasing curve even at small imaginary part of eigenvalues. The deviation is the greater the smaller is the eigenvalue real part modulus and the greater is its multiplicity and the gain coefficient. An analytical solution to the problem of free motion system state vector norm is derived, the solution correctness is verified by computer modeling.
Keywords: complex-conjugate eigenvalues, modified Butterworth distribution, sectoral restriction, modified Jordan form, multiplicity, free motion, norm, deviation

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