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This article deals with the distributed state estimation problem for linear systems in networks with cooperative interactions and antagonistic interactions, where the cooperative interactions and the antagonistic interactions are characterized by the positive weights and the negative weights, respectively. Due to the coexistence of the cooperative interactions and the antagonistic interactions, the existing methods based on the non-negatively weighted graph become not applicable. First, a partition method of the nodes and a decomposition form of the system matrices are introduced. Then a new form of distributed observers is proposed in the network with cooperative interactions and antagonistic interactions. Necessary and sufficient conditions, which guarantee the existence of proposed distributed observers, are presented. In particular, when the communication network is cooperative, the proposed method is suitable for two cases, that is, the nodes in each independent strongly connected component are jointly detectable, or each node is jointly detectable with its neighbors. Finally, three examples are simulated to illustrate the effectiveness of the proposed methods.
Gao et al. (Thu,) studied this question.