摘要
本文应用Liapunov函数方法,研究了复合大系统dx/(dt)=P(t)A(t)x的稳定性,在此基础上,给出了周期大系统dx/dt=P(t)A(t)x+f(x)存在平稳振荡的充分条件,并且给出了非线性周期复合大系统dx/dt=P(t)A(t)x+g(t,x)的解的有界性和周期解的存在性的充分条件,改进了文[3～6]的有关结果。
In this paper, by means of Liapunov function, we study the stability of composite system dx/dt =P(t)A(t)x, furthermore, we study the existence of stationary oscillation of periodic composite system dx/dt=P(t)A(t)x+f(t), and the bundedness of solution and existence of periodic solution of periodic composite system dx/dt=P(t)A(t)x+g(t,x).
出处
《新疆大学学报（自然科学版）》
CAS
1992年第3期19-25,共7页
Journal of Xinjiang University(Natural Science Edition)
关键词
大系统
Liadunov函数
周期解
large-scale system
Liapunov function
periodic solution
stationary oscillation
