  For ordinary differential equations and functional differential equations the
following result is well known. Suppose any solution is bounded on the
half-line for each bounded on the half-line right-hand side. Then under certain
conditions the equations is exponentially stable.
  We prove the same result for a delay differential equation
  $$ \dot{x}(t) + \sum_{i=1}^k A_i (t)x[h_i(t)] = f(t), $$
  with impulses
  $$ x(\tau_i + 0) = B_i x(\tau_i - 0) $$
  at fixed moments $\tau_i$. The proof is based on a solution representation
formula obtained here.
