Recursive set-membership filtering for two-dimensional shift-varying systems with FlexRay protocol and hybrid cyber attacks

The problem of recursive set-membership filter design for two-dimensional (2-D) systems subject to FlexRay communication protocol and hybrid cyber attacks (HCAs) is investigated in this article. The FlexRay protocol that integrates time-triggered and event-triggered mechanisms and involves a series of pre-defined communication cycles based on bidirectional metrics is developed to alleviate the network bandwidth load. Furthermore, the envisioned system is exposed to false data injection and denial-of-service attacks that occur in a randomized manner. Subsequently, the dynamic filtering error system (FES) subject to bidirectional evolutionary HCAs and FlexRay scheduling protocol is constructed. Then, sufficient conditions are obtained such that the dynamic FES consistently resides within an ellipsoidal set by utilizing double mathematical induction and recursive linear matrix inequalities (RLMIs). Moreover, the optimal filtering algorithm is given by minimizing the ellipsoidal constraints from the perspective of the traces of the matrix. The effectiveness of the presented recursive set-membership filter design approach is validated by a long-distance transmission line example.