Distributed State Estimation for Discrete-Time Linear Systems: A Canonical Decomposition-Based Approach

In this article, we are concerned with the problem of distributed state estimation for discrete-time linear systems using a network of agents, where the measurement of each agent suffers from the lack of detectability with the system dynamics. The existing results on this topic require stringent condition either on the network connectivity or on the detectability. In contrast, a new form of distributed observer, which ensures that all agents asymptotically estimate the system state under the mild network connectivity condition without increasing the need for the detectability condition, is proposed. Necessary and sufficient conditions for the existence of the proposed distributed observer are established. The key to the proposed method is a refined canonical decomposition form of the coefficient matrices of the system which is introduced leveraging the real Jordan canonical form, the Popov–Belevitch–Hautus test, the matrix permutation, and the observable decomposition. The methodology is applied to estimate the positions of a group of Pendubots to demonstrate its effectiveness.