In this paper, we study the problem of interval-observer based controller design for switched linear systems with disturbance and measurement noise. First, we propose the definition of finite-time interval-observersfor switched systems and construct finite-time interval-observers for switched linear systems with observer-statedependent switching strategy by giving the ranges of the external disturbance and the measurement noise. Then,by using multiple Lyapunov functions method, some sufficient conditions are provided to guarantee the existenceof the finite-time interval-observers under maximum constraints, and at the same time, based on the proposed sufficient conditions, the observer gains are given and the corresponding sliding motion issue is also solved. Afterthat, we design an interval-observer-based feedback controller for the switched systems. Different from the traditional observer-based controller with state-dependent switching signal designed in most literatures, the controllerdesigned in the paper is based on interval-observer with observer-state-dependent switching signal. Compared withthe traditional observers, the interval-observers are robust to large uncertainties and can provide the ranges of thesystem states in any time. Finally, the feasibility of the proposed method is verified by two numerical examples.