The stability of limit cycles in nonlinear systems |
| |
| Authors: | Ali Ghaffari Masayoshi Tomizuka Reza A. Soltan |
| |
| Affiliation: | (1) Faculty of Mechanical Engineering, K. N. Toosi University of Technology, Pardis St., Vanak Sq., Tehran, 16569 83911, Iran;(2) Department of Mechanical Engineering, University of California at Berkeley, 5100B Etcheverry Hall, Mailstop 1740, Berkeley, CA 94720, USA |
| |
| Abstract: | In this paper, a necessary condition is first presented for the existence of limit cycles in nonlinear systems, then four theorems are presented for the stability, instability, and semistabilities of limit cycles in second order nonlinear systems. Necessary and sufficient conditions are given in terms of the signs of first and second derivatives of a continuously differentiable positive function at the vicinity of the limit cycle. Two examples considering nonlinear systems with familiar limit cycles are presented to illustrate the theorems. |
| |
| Keywords: | Limit cycle Existence Stability Nonlinear systems First and second derivatives |
| 本文献已被 SpringerLink 等数据库收录！ |
|
