A new fuzzy Lyapunov function approach to fault detection of fuzzy systems

This article constructs a new fuzzy Lyapunov function (LF) scheme to fault detection (FD) of discrete-time T-S fuzzy models. A fuzzy FD observer is first established to generate residual signals. Then, based on the proposed fuzzy LF, where the membership functions (MFs) of the fuzzy Lyapunov matrix in LF can be used to characterize its forward ones, sufficient conditions in terms of linear matrix inequalities (LMIs) are obtained to guarantee the FD performance of the FD systems. Unlike the existing fuzzy LF methods that depend on the MFs in the T-S models and their forward differences, the Lyapunov inequality in the proposed one can avoid the occurrence of forward differences about the MFs, thus overcoming the shortcomings of the existing results. Finally, two simulation results are shown to verify that the presented technical solution is effective and can achieve better FD results than the existing ones with quadratic LFs.