Consider the system of functional differential equations with impulses
where, as usual, . It is assumed that zero is a solution to this system.
Using Lyapunov-like functionals, sufficient conditions are found to prove that the trivial solution is exponentially stable. The paper also contains several examples; in particular, it is shown that an unstable linear delay-differential equation may become exponentially stable by adding a suitable impulsive (nondelayed) perturbation.