In this paper, we present a hybridization method for sta- bility analysis of switched linear hybrid system (LHS), that constructs a switched system with polyhedral inclusion dy- namics (PHS) using a state-space partition that is specific to stability analysis. We use a previous result based on quanti- tative predicate abstraction to analyse the stability of PHS. We show completeness of the hybridization based verifica- tion technique for the class of asymptotically stable linear system and a subclass of switched linear systems whose dy- namics are pairwise Lipschitz continuous on the state-space and uniformly converging in time. For this class of systems, we show that by increasing the granularity of the region par- tition, we eventually reach an abstract switched system with polyhedral inclusion dynamics that is asymptotically stable. On the practical side, we implemented our approach in the tool Averist, and experimentally compared our approach with a state-of-the-art tool for stability analysis of hybrid systems based on Lyapunov functions. Our experimental results illustrate that our method is less prone to numerical errors and scales better than the traditional approaches. In addition, our tool returns a counterexample in the event that it fails to prove stability, providing feedback regarding the potential reason for instability. We also examined heuristics for the choice of state-space partition during refinement.