Co-design of adaptive polynomial event-triggered scheme and polynomial fuzzy fault detection filter for polynomial fuzzy systems

For networked polynomial fuzzy systems (PFSs), the co-design of the adaptive polynomial event-triggered scheme (APETS) and the fault detection scheme is investigated in this paper. The novel APETS is adopted to reduce the burden of communication where the singularity problem of the adaptive threshold is avoided and the design freedom is enhanced through polynomial weight matrices. Considering the unmatched premise variables (PVs) caused by APETS and the transmission delay, asynchronous filters are established while different membership functions (MFs) and the fuzzy rule numbers (FRNs) from the original system are utilized for more flexible filters. In the solution process, considering the specificity of the form of the stability analysis constraints, local stability is discussed by a permutation-based approach. Finally, two simulation examples are adopted to verify the feasibility and efficacy of the posed method in terms of reducing conservativeness, improving design flexibility and fault detection performance, and the effect of the filter matrix order is also analyzed.