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Abstract

In this paper, the set-membership filtering problem is investigated for a discrete-time system with unknown-but-bounded noises and filter-and-forward (FaF) successive relays. The FaF successive relay adopts two relay nodes, each embedded with a linear filter, to alternately receive measurements from the sensor and forward the outputs of the relays’ filters to the remote filter. By introducing an auxiliary variable, a unified model is established to describe the dynamics of both relay nodes. To handle the inter-relay interference (IRI) in the successive relay, a system transformation method is proposed where IRI is reformulated as the unknown input with a full-column-rank distribution matrix. Then, a new unknown input observer-based set-membership filter is constructed for the successive relay. With the help of the recursive linear matrix inequality technique, set-membership filtering strategies are jointly developed for the FaF relay and the discrete-time system to get ellipsoid sets containing the true state of interest. Moreover, the desired filter gain matrices are further obtained by solving constraint optimization problems. Finally, the effectiveness of the proposed filtering method with a FaF successive relay mechanism is verified by a three-order RLC circuit system.