STABILITY ANALYSIS FOR LINEAR DELAY DIFFERENTIAL EQUATIONS AND NUMERICAL EXAMPLES

摘要

The asymptotic stability of delay differential equation x′ (t) = Ax (t) + Bx (t_τ) is concerned with, where A, B∈ C~(dxd) are constant complex matrices, x(t_τ) = (x_1 (t - τ_1), x_2 (t -τ_2 ),. . . , x_d (t - τ_d))~T, τ_k>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∈C~(dxd) are constant complex matrices and τ>0 stands for constant delay. Numerical examples are showed to check the results which are more general than those already reported.