李彦敏, 陈向炜. 二阶广义自治Birkhoff系统的全局稳定性[J]. 云南大学学报(自然科学版), 2013, 35(5): 638. doi: 10.7540/j.ynu.20120690
引用本文: 李彦敏, 陈向炜. 二阶广义自治Birkhoff系统的全局稳定性[J]. 云南大学学报(自然科学版), 2013, 35(5): 638. doi: 10.7540/j.ynu.20120690
LI Yan-min, Chen Xiang-wei. Global stability of second order autonomous generalized Birkhoff system[J]. Journal of Yunnan University: Natural Sciences Edition, 2013, 35(5): 638. DOI: 10.7540/j.ynu.20120690
Citation: LI Yan-min, Chen Xiang-wei. Global stability of second order autonomous generalized Birkhoff system[J]. Journal of Yunnan University: Natural Sciences Edition, 2013, 35(5): 638. DOI: 10.7540/j.ynu.20120690

二阶广义自治Birkhoff系统的全局稳定性

Global stability of second order autonomous generalized Birkhoff system

  • 摘要: 利用Liapunov函数法和Кpacoвcий方法研究二阶广义自治Birkhoff系统的全局渐近稳定性.首先给出该系统Liapunov函数V的形式,然后证明了Liapunov函数对时间的导数V与矩阵F(a)的关系,进一步给出了判断该系统全局渐近稳定性的命题,最后举例说明结果的应用.

     

    Abstract: The global asymptotic stability of second order autonomous generalized Birkhoff system is studied by using of Liapunov function method and Кpacoвcий method.Firstly,the form of Liapunov function V of the system is given.Then,the relations between the derivative V of Liapunov function V with respect to time t and the matrix F(a) are verified,and the proposition of global asymptotic stability of the system is proposed.Finally,an example is given to illustrate the application of the result.

     

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