%0 Journal Article
%A Vunder, Nina A.
%A Ushakov , Anatoliy V.
%D 2015
%I Begell House
%K oscillatory process, multiplicity factor, deflection magnitude, state matrix, complex conjugate eigenvalues
%N 11
%P 18-35
%R 10.1615/JAutomatInfScien.v47.i11.20
%T Investigation of Continuous Systems Oscillatory Processes Created with the Multiplicity Factor of the Eigenvalues of the State Matrices
%U http://dl.begellhouse.com/journals/2b6239406278e43e,38d51d0f167e9830,071b740c40ba9e72.html
%V 47
%X 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.
%8 2016-01-28