Journal of Applied Mathematics
Volume 2013 (2013), Article ID 712932, 7 pages
Research Article

Existence and Uniqueness of the Exponentially Stable Limit Cycle for a Class of Nonlinear Systems via Time-Domain Approach with Differential Inequality

1Department of Electrical Engineering, I-Shou University, No.1, Sec. 1, Syuecheng Road, Dashu District, Kaohsiung City 84001, Taiwan
2Institute of Manufacturing Information and Systems, National Cheng Kung University, Tainan, Taiwan

Received 29 November 2012; Revised 8 March 2013; Accepted 16 March 2013

Academic Editor: Samir H. Saker

Copyright © 2013 Yeong-Jeu Sun et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The concept of the exponentially stable limit cycle (ESLC) is introduced, and the ESLC phenomenon for a class of nonlinear systems is explored. Based on time-domain approach with differential inequality, the existence and uniqueness of the ESLC for such nonlinear systems can be guaranteed. Besides, the period of oscillation, the amplitude of oscillation, and guaranteed convergence rate can be accurately estimated. Finally, two numerical simulations are provided to illustrate the feasibility and effectiveness of the obtained result.