具有时滞的变系数系统也称为时变线性微分差分系统.秦元勋,王联,王慕秋采用冻结系数的方法,廖晓昕利用迭代法,张学铭构造二次型加积分项的函数,徐道义利用比较定理与向量函数(后来,文[5]也采用了此法)分别研究了这类系统的稳定性.本文则建立了较向量函数更为灵活的广义向量 V 函数法,并利用它给出了具有滞后的线性单结构系统与复合系统以及一些特殊的非线性系统稳定性的条件.
This paper first gives necessary and sufficient conditions of asymptotic stability independent of delay (ASi. o. d. ) of a certain class of symmetric differential systems with commensurate or non -commensurate delays. These conditions give equivalent relationship between the Asi. o. d. of delay systems and the asymptotic stability of ordinary differential systems with special complex coefficients. Then a sufficient condition for the Asi. o.d. of symmetric retarded system is obtained in terms of negative definiteness of a real symmetric matrix. Finally, examples are shown to demonstrate the effectiveness of the proposed method.
