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Exponential stability for impulsive delay differential equations by Razumikhin method. (English) Zbl 1084.34066

This paper deals with the exponential stablity of the solutions of the following impulsive delay differential equation \[ \dot x(t)=f(t,x_t), \;\;t\not=t_{k}, \]
\[ \Delta x(t)=I_{k}(t,x_{t^{-}}), \;t=t_{k}, \;k\in \mathbb{N}, \]
\[ x_{t_{0}}=\phi. \] The proofs are based on the Razumikhin method. Some examples illustrating the results are presented.

MSC:

34K20 Stability theory of functional-differential equations
34K45 Functional-differential equations with impulses
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