Reaching Distributed Interval State Estimation on Discrete-Time LTI Systems

The distributed state estimation problem of a discrete-time linear time-invariant system is considered in the presence of external disturbances and measurement noise. In this scenario, where only the bounding information of the external disturbance and measurement noise is known, an initial design of a distributed interval observer is implemented to provide a set of intervals within which the state of the system locates, subject to certain requirements on relevant matrices. Subsequently, the Internal Positive Representation technique is introduced to eliminate the aforementioned requirements, so that a distributed observer can be accomplished, with the only prerequisite being collectively detectable of the output measurements of the sensor network. Finally, two examples are proposed to illustrate the effectiveness of the theoretical results.