Title :
Higher harmonics and verification of limit cycle stability in autonomous nonlinear systems
Author :
Qiu, Shui-Sheng ; Filanovsky, I.M.
Author_Institution :
South China Univ. of Technol., Guangzhou, China
Abstract :
A method for verification of limit cycle stability in autonomous nonlinear systems is proposed. The oscillation is represented in an exponential form and the operator equation of perturbation is obtained The third harmonic increments are eliminated from this equation using the steady-state third harmonic linearized equation. Then the operator is simplified and real and imaginary parts are separated to obtain a system of two first order linear differential equations for the first harmonic amplitude increments. The characteristic equation of this last system is used for verification of the limit cycle stability.
Keywords :
harmonics; limit cycles; linear differential equations; nonlinear systems; perturbation techniques; stability; autonomous nonlinear systems; characteristic equation; exponential oscillation form; first harmonic amplitude increments; first order linear differential equations; limit cycle stability; operator equation; perturbation; third harmonic increments; Differential equations; Limit-cycles; Nonlinear equations; Nonlinear systems; Oscillators; Polynomials; Stability; Steady-state; Zinc;
Conference_Titel :
Circuits and Systems, 1997. Proceedings of the 40th Midwest Symposium on
Print_ISBN :
0-7803-3694-1
DOI :
10.1109/MWSCAS.1997.662364
