一阶双滞量时滞方程零解渐进稳定的充要条件

A necessary and sufficient condition for asymptotic stability of first order delay equation with two delays

考虑以下方程x.(t)+I(b)x(t)+bx(t-τ)+cx(t-2τ)=0其中b,c,τ是常数,并且τ>0,bc≠0,I(b)=2 0148τ[27(bτ)4-576(bτ)2-1 024],建立了方程零解渐进稳定的充要条件,易于检验和应用.

Considers the following equationx（t）＋I（b）x（t）＋bx（t-τ）＋cx（t-2τ）=0 where b,c and τ are constants,and τ〉0,bc≠0,I（b）=2 0148τ[27（bτ）4-576（bτ）2-1 024]. In this paper, a necessary and sufficient condition for zero solution of the equation to be asymptotically stable is established ,which is easy to test and apply.