Geodesic
Sufficient conditions for absolute asymptotic stability of linear equations in a Banach space
Matematičeskie zametki, Tome 17 (1975) no. 6, pp. 919-923 Cet article a éte moissonné depuis la source Math-Net.Ru

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For a linear differential equation of the type \begin{equation} \frac{dx}{dt}=A_0x(t)+A_1x(t-\Delta_1)+\dots+A_nx(t-\Delta_n)\tag{1} \end{equation} we establish the following \underline {THEOREM}. If $$ \overline{\bigcup_{|z_1|=\dots=|z_n|=1}\sigma\Bigl(A_0+\sum_{k=1}^nz_kA_k\Bigl)}\subset\{\lambda:\operatorname{Re}\lambda<0\}, $$ then system (1) is absolutely asymptotically stable. 
@article{MZM_1975_17_6_a9,
     author = {V. E. Slyusarchuk},
     title = {Sufficient conditions for absolute asymptotic stability of linear equations in {a~Banach} space},
     journal = {Matemati\v{c}eskie zametki},
     pages = {919--923},
     year = {1975},
     volume = {17},
     number = {6},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1975_17_6_a9/}
}
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V. E. Slyusarchuk. Sufficient conditions for absolute asymptotic stability of linear equations in a Banach space. Matematičeskie zametki, Tome 17 (1975) no. 6, pp. 919-923. http://geodesic.mathdoc.fr/item/MZM_1975_17_6_a9/