脉冲泛函微分方程稳定性的新准则

New Criteria for Stability of Impulsive Functional Differential Equations

研究了脉冲泛函微分方程x′(t)=F(t,x(.)),t≥0,t≠tk,Δx(tk)=I(tk,x(t-k)),k=1,2,….的稳定性.采用Liapunov泛函方法和Jensen不等式,通过改进Lyapunov泛函的下界,获得了这类方程的零解一致渐近稳定的新准则,改进了已有文献中的相应结果.

This paper considers a class of impulsive functional differential equations of the form {x′（t）=F（t,x（·））,t≥0,t≠tk,△x（tk）=I（tk,x（tk-））,k=1,2,….By using the Liapunov functional method and Jensen＇s inequality, some new stability criteria are obtained based on the improvement of the lower bound of Liapunov functional. The corresponding results in the literature are improved.