The design of event-triggered fault detection observers has been discussed in this chapter, and several existing methods for dealing with the asynchronous problems of premise variables in T-S fuzzy systems in networked environments have also been introduced, please refer to Refs. [1–6], including partition method, non-PDC method, etc. At the same time, it is pointed out that there are limitations and defects in these types of methods, and a new matching membership function strategy is proposed to handle the mismatch of premise variables in view of the shortcomings of the existing non-PDC methods, thereby solving the design of event-triggered fault detection observers.