Inscrição na biblioteca: Guest
Portal Digital Begell Biblioteca digital da Begell eBooks Diários Referências e Anais Coleções de pesquisa
Journal of Automation and Information Sciences
SJR: 0.232 SNIP: 0.464 CiteScore™: 0.27

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

Volumes:
Volume 51, 2019 Volume 50, 2018 Volume 49, 2017 Volume 48, 2016 Volume 47, 2015 Volume 46, 2014 Volume 45, 2013 Volume 44, 2012 Volume 43, 2011 Volume 42, 2010 Volume 41, 2009 Volume 40, 2008 Volume 39, 2007 Volume 38, 2006 Volume 37, 2005 Volume 36, 2004 Volume 35, 2003 Volume 34, 2002 Volume 33, 2001 Volume 32, 2000 Volume 31, 1999 Volume 30, 1998 Volume 29, 1997 Volume 28, 1996

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

RESUMO

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.