It will be presented a general framework for a quantitative predicate abstraction for stability analysis of hybrid systems. Predicate abstraction consists of constructing a finite abstract system from a concrete system, such that the former one simulates the latter system. Simulation relations preserve several discrete-time properties, but for stability preservation some continuity constraints are required. It will be proposed a quantitative version of predicate abstraction and provided a formal connection between the abstract system and the concrete hybrid system by using the continuous simulations. Finally, it will be instantiated the general framework to the class of piecewise linear dynamical systems, and illustrated on an example.