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Journal of Automation and Information Sciences
SJR: 0.232 SNIP: 0.464 CiteScore™: 0.27

ISSN Imprimir: 1064-2315
ISSN On-line: 2163-9337

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Journal of Automation and Information Sciences

DOI: 10.1615/JAutomatInfScien.v47.i11.20
pages 18-35

Investigation of Continuous Systems Oscillatory Processes Created with the Multiplicity Factor of the Eigenvalues of the State Matrices

Nina A. Vunder
Saint Petersburg State University of Information Technologies, Mechanics and Optics, Saint Petersburg (Russia)
Anatoliy V. Ushakov
St. Petersburg State University of Information Technologies, Mechanics and Optics Russia


The stable continuous systems whose state matrix has spectra of multiple eigenvalues are considered. The problem is solved at eigenvalues multiplicity equal to the state vector dimension, first consideration is given to the case of real eigenvalues, and then − the case of complex conjugate ones. It was shown that if a modulus of the real eigenvalue was less than unity, then in the trajectories of the system free motion by the norm of its state vector there is observed a deflection alternating by monotone convergence of trajectory to zero. It was established that the deflection magnitude was the larger the smaller was the modulus of the real eigenvalue and the larger was its multiplicity. If the continuous system state matrix has the spectrum of complex conjugate eigenvalues, then at the value of the real part of complex conjugate eigevalue smaller than unity, as in the case of eigenvalues real spectrum, there occur the deflections of trajectories whose magnitude is the larger the smaller is its modulus and the larger is its multiplicity.