By Topic

On verification of limit cycle stability in autonomous nonlinear systems

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$33 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

2 Author(s)
S. -S. Qui ; South China Inst. of Technol., Guangzhou, China ; I. M. Filanovsky

A method for verification of limit-cycle stability in autonomous nonlinear systems is proposed. The method is applicable to systems with limit cycles described by a sinusoid (main oscillation) with small addition of harmonics. The main oscillation is represented in exponential form and is substituted into the nonlinear part of the initial differential equation. The nonlinear part is linearized with respect to the amplitude perturbations and the operator equation for the perturbations is obtained. Then the terms representing derivatives higher than first order are omitted in the corresponding operators and the real and imaginary parts of the simplified operator equation are separated. This results in two first-order linear differential equations for the increments of the main oscillation amplitudes. The differential equations are used for verification of the limit-cycle stability. The case of asynchronous perturbation is considered as well

Published in:

IEEE Transactions on Circuits and Systems  (Volume:35 ,  Issue: 8 )