Distributed non-fragile set-membership filtering for nonlinear systems under fading channels and bias injection attacks

In this paper, the secure distributed set-membership filtering problem is investigated for general nonlinear system over wireless sensor networks. For the purpose of getting close to practical wireless sensor networks, both the bias injection attacks and the channel fading of wireless communication are taken into account in the procedure of filter design. By employing linear matrix inequality (LMI) technique and Taylor's expansion formula, the nonlinearity, the channel fading, the bias injection attacks and the non-fragile are handled simultaneously in the set-membership filtering framework and the filter design problem is addressed. For the pre-specified filtering performance, sufficient conditions are obtain to ensure the existence of desired filter, where the filter gains are acquired via solving certain recursive LMI. Furthermore, in order to look for the locally best performance, an optimal algorithm is proposed. Finally, a simulation example is given to demonstrate the effectiveness of our proposed secure filtering algorithm.