Abstract This paper proposes a two-step interval estimation method for continuous-time switched linear systems subject to unknown but bounded disturbance and measurement noise. We first use an L∞ norm-based approach to attenuate the effect of uncertainties in observer design. Then, based on the obtained observer, interval estimation can be achieved via analyzing the bounds of estimation error. The proposed method is intuitive and independent of cooperativity constraint, which is main restriction of interval observer theory. The performance of the proposed method is demonstrated through a numerical simulation.