This paper proposes a two-step distributed interval estimation method for continuous-time linear time-invariant (LTI) systems subject to unknown but bounded disturbance and measurement noise. First, a network of local observers is designed to obtain point-wise estimation. Second, interval estimation is obtained based on the point-wise estimation and peak-to-peak analysis. The conditions of the observer design and the peak-to-peak analysis are formulated as linear matrix inequalities, which can be solved efficiently. Compared with the distributed interval observers designed using the monotone system theory, the proposed method has less restrictive design conditions and hence broader application scopes. Moreover, the parameter matrices in the proposed method can be optimized to obtain tight interval estimation. A numerical simulation is given to illustrate the performance of the proposed method.
