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Stability criteria for linear delay differential equations. (English) Zbl 0894.34064
Linear delay differential systems of the form $\dot x(t)= A(t)x(t-\tau (t))$ with a continuous $$n\times n$$-matrix-valued function $$A$$ defined on $$[t_0, \infty)$$ and with a continuous $$\tau : [t_0, \infty) \mapsto [0,r]$$, $$0 < r =\text{const}$$ are considered.
Conditions for the stability and asymptotic stability of the zero solution of the given equation are presented. The results are used for discussing the equation $$\dot x(t)= \dfrac {\sin t}{t^{\alpha }}x(t- r)$$ in dependence on the parameter $$\alpha$$.

##### MSC:
 34K20 Stability theory of functional-differential equations