Distributed interval estimation for continuous-time linear systems based on multi-hop decomposition and interval analysis

This paper investigates the distributed interval estimation problem for collectively observable continuous-time linear time-invariant (LTI) systems subject to unknown but bounded disturbance and measurement noise. To address this problem, a novel two-step interval estimation approach is proposed, which establishes new conditions for the design of the distributed observer for point-wise estimation, followed by interval estimation via interval analysis. By applying multi-hop staircase decomposition, a distributed observer, consisting of a set of local observers that only have access to limited output information, is designed in a cascaded way. After the distributed observer has been designed, an interval estimation is obtained by applying interval analysis methods and interval observer principles. Compared with the previous distributed interval observer design methods, the proposed approach requires milder assumptions and less information exchange. In addition, the distributed interval estimation can always be implemented without any prerequisites except for the collectively observable condition. Finally, numerical simulations are given to support and illustrate the theoretical results.