In this paper a new systematic switching control approach to adaptive stabilization of linear time-varying (LTV) discrete-time systems is presented. A feature pf the localization-based method is its high model falsification capability, which in the case of LTI systems is manifested as the rapid convergence of the switching controller. We believe that the proposed method may help pave the way for design of practical adaptive switching controllers applicable to a wide range of linear time-invariant and time-varying systems.