Interval estimation for discrete‐time linear systems based on unknown input observer and reachability analysis

Abstract This paper presents an interval estimation method for discrete‐time linear systems with disturbance and measurement noise. First, comparing the existing results, an unknown input observer (UIO) with fewer conservative conditions is designed to estimate the system state. In order to improve the estimation accuracy, a decoupling approach, which can be used to decouple the disturbance matrix, is proposed to overcome the effect of disturbances in the error system. Then, technology is introduced to enhance the robustness of the error system. Subsequently, based on the UIO and the decoupling approach, interval estimation of the system state can be attained through reachability analysis. Moreover, the proposed method exhibits a higher precision and lower complexity in comparison to the existing approaches. Eventually, the simulation results are presented to verify the efficiency of the proposed method.