In this paper, we report some new results on practical asymptotic stabilizability of switched systems consisting of time-invariant subsystems. After formally introducing the concept of practical asymptotic stabilizability, we propose some sufficient conditions based on energy functions. We then point out that the vector fields of a switched system can be decomposed into two parts, namely, vector fields corresponding to a common equilibrium and vector fields corresponding to integrator dynamics. Such a decomposition makes it possible to study the relationship between conventional asymptotic stabilizability and practical asymptotic stabilizability of switched systems. Based on the decomposition, we present methods for estimating the region of attraction for switched affine systems.