一类时滞微分方程滞后量的估计  

The Estimates of Delays for a Class of Differential Delay Equations

作　　者：辜建德[1] 

机构地区：[1]厦门大学计算机与系统科学系

出　　处：《厦门大学学报（自然科学版）》1991年第2期119-124,共6页Journal of Xiamen University：Natural Science

基　　金：国家自然科学基金

摘　　要：考虑时滞微分方程 x(t)=A(t)x(t)+B(t)x(t—τ)和 x(t)=A(t)x(t)+B(t)x(t—τ)+H((x(t),x(t-τ)),其中 A(t)和B(t)是n×n矩阵,关于t连续,H:R~?×R~?→R~?是非线性连续函数,是后一系统的扰动函数。本文中,对两个系统分别给出了滞后量的估计τ_0,使得当 0≤τ≤τ_0时,前系统渐近稳定,后系统在经常扰动下是稳定的。估计中运用了新的方法,因此,估计较少保守性。改进和推广了有关文献中的结果。Consider the systems of differential delay equationsX(t) = A(t)X(t)+B(t)X(t-τ),andX(t)=A(t)X(t)+B(t)X(t-τ) + H(X(t),X(t-τ)) Where A(t)and B(t) are n×n matrices, continuous with respecf to t, H :Rn×Ra→Rn is a nonlinear continuous function, a disturbing function of two. In the paper, the estimates TO of the delays the first system is asymptotically stable, the second system is stable unaer constantly disturbing. Some new methods are used in the estimates so that the estimates are less conservative, the resultsin some references are improved and generalized.

关 键 词：时滞微分方程 滞后量 稳定性 

分 类 号：O175[理学—数学]