This paper studies the robust exponential input-to-state stability (robust e-ISS) for impulsive systems. New notions of input-to-state exponent (IS-e) and e-property are proposed. Based on the established relation between IS-e and e-property, and the method of variation of constants formula, the equivalent conditions for robust e-ISS have been derived. Then the notion of robust event-e-ISS is defined. The sufficient conditions and the robust regions for robust e-ISS and robust event-e-ISS are also derived by using the IS-e of every subsystem. It shows the whole system may have robust event-e-ISS while every subsystem may have no ISS. It also shows the external disturbances may lead to relatively small robust regions. The results are then specialized to derive the equivalent conditions of interval e-ISS for interval impulsive systems. As an application, the result is used to test the ISS for a controlled micro-grid. © 2014 Elsevier B.V. All rights reserved.