The asymptotic stability of delay differential equation x′(t) =Ax(t)+Bx(tτ)is concerned with,where A,B ∈ Cd×d are constant complex matrices, x(tτ)=(x1(t-τ1),x2(t-τ2 )，… xd (t-τd))τ, τk>0 (k=1，…，d) stand for constant delays.Two criteria through evaluation of a harmonic function on the boundary of a certain region are obtained.The similar results for neutral delay differential equation x′(t)=Lx(t)+Mx(t-τ)+Nx′(t-τ) are also obtained,where L,M and N ∈ Cd×d are constant complex matrices and τ>0 stands for constant delay.Numerical examples are showed to check the results which are more general than thos ealready reported.
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