The paper provides a computation-oriented necessary and sufficient condition for the global exponential stability of linear impulsive systems, whose impulsions are assumed to occur quasi-periodically. Based on the set-theoretic conditions for robust stability of uncertain linear systems, the existence of polyhedral Lyapunov functions is proved to be necessary and sufficient for global exponential stability of quasi-periodic linear impulsive systems. A constructive method is developed for testing the stability of the system and for computing set-induced polyhedral Lyapunov functions. The method leads to an algorithm whose complexity is similar to the standard algorithm related to discrete-time parametric uncertain systems with the state matrix belonging to a convex polytopic set.