The reachable set estimation and control problems for continuous-time switched linear systems are addressed in this paper. First, a general result on reachable set estimation for switched system is proposed based on a Lyapunov function approach. Then, with the help of a class of time-scheduled Lyapunov functions, a numerically tractable sufficient condition ensuring the system state bounded in a prescribed set is derived for switched systems under dwell time constraint. Moreover, a time-scheduled state feedback controller is designed to ensure the state trajectories of the closed-loop system are confined in a prescribed set. Finally, a networked control system subject to packet dropouts is modeled as a switched system with dwell time constraints, and the controller design problem is studied as an application of our results.