In this chapter, we address the challenge of designing an interval state estimation for discrete-time linear switched systems in the Unknown But Bounded Error (UBBE) context. The considered systems are subject to unknown but bounded disturbances and measurement noise in predefined zonotopes. The main contribution lies in the development of a two-step interval state estimation approach which combines a robust observer design providing more degrees of design freedom with a zonotopic analysis technique. First, we design a switched observer based on the \(H_\infty \) formalism, which reduces the impact of unknown uncertainties and provides a point estimate of the system state. The observer gains are computed by solving a Linear Matrix Inequality (LMI) obtained using multiple Lyapunov functions, while adhering to the Average Dwell Time (ADT) concept. Second, we combine the robust point estimation with zonotopic analysis techniques to achieve an interval estimation. The proposed approach is evaluated through simulation results on an academic example, demonstrating its effectiveness and advantages over existing methods.