Finite-horizon distributed set-membership filtering with dynamical bias and DoS attacks under binary encoding schemes

In this work, we cope with the design issue of finite-horizon distributed set-membership filters concerning a set of time-varying systems (TVSs) over sensor networks (SNs). The system to be discussed is suffering from dynamical bias and unknown but bounded noise. The binary encoding schemes (BESs) are utilized in the data transmission through SNs from neighbors to the intelligent sensor nodes, which exhibit robustness to some degree due to usage of the binary data. Both random bit errors caused by channel noises and denial of service (DoS) attacks reflecting network vulnerability are considered that may arise and lead to signal distortion in the transmission process of the binary bit string. In the framework of adopting BESs, our aim is to realize the distributed set-membership filtering for TVSs over SNs limited by dynamical bias and DoS attacks. Sufficient conditions, relying on the solvability of a class of recursive linear matrix inequalities, are obtained for the presence of the expected time-varying distributed set-membership filters. Furthermore, an additional optimization issue is constructed to find the minimal ellipsoids (on the basis of matrix trace) to obtain the best filtering performance. Eventually, a numerical simulation instance is provided to verify the availability of the presented design strategy of finite-horizon distributed set-membership filters.