Distributed Interval Estimation for Continuous-Time Linear Systems Based on Robust Observer and Interval Analysis

This article aims at investigating distributed interval estimation methods for continuous-time linear time-invariant (LTI) systems. By allying a robust observer design method and interval analysis techniques, we develop a novel two-step interval estimation method for LTI systems whose outputs are measured by a series of nodes connected via a given directed graph. First, a distributed observer formed by a group of local observers is designed via an $H_{\infty } $ approach to obtain an accurate point-valued estimation. This estimation is completed by a reliable interval-valued estimation achieved by a rigorous set-valued analysis of the estimation error dynamics. In order to further enhance the accuracy of the estimated intervals, an elimination by inconsistency technique is applied to characterize the smallest common interval containing the actual state vector of the system. Compared with the existing distributed interval observer approaches, the proposed method can effectively enhance the tightness of the estimated state intervals. Simulation results are shown to support the theoretical findings.