The stability of limit cycles in nonlinear systems

被引：0

作者：

Ali Ghaffari

Masayoshi Tomizuka

Reza A. Soltan

机构：

[1] K. N. Toosi University of Technology,Faculty of Mechanical Engineering

[2] University of California at Berkeley,Department of Mechanical Engineering

来源：

Nonlinear Dynamics | 2009年 / 56卷

关键词：

Limit cycle; Existence; Stability; Nonlinear systems; First and second derivatives;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

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.

引用

页码：269 / 275

页数：6