Designing a Completely Distributed Interval Observer for the LTI System

In this article, the distributed interval observer design problem for a continuous-time linear time-invariant system with unknown external disturbance and measurement noise is revisited. By performing detectability decomposition for partial outputs of each sensor from the system matrix, a classical interval observer and an internally positive representation-based interval observer are designed for the detectable and the undetectable subsystems, respectively, which reduces the order of the resulting distributed interval observer. Furthermore, with a dynamic coupling gain on the communications among the interval observers, a completely distributed interval observer is designed without any prerequisite, except for the joint detectability of the partial measurements and the strong connectivity of the properly defined directed sensor network. Finally, after detailed analyses, the theoretical results were validated through numerical simulations.