In Chap. 3 and this chapter, the \(H_{\infty }\) filtering problems of discrete-time T-S fuzzy systems were studied respectively, and the external disturbances in systems are assumed to be energy bounded. However, it should be noted that the above mentioned results are obtained based on the traditional sampling data, that is, the data is sampled with a fixed period, which is named the time-triggered mechanism [1–3]. Although this mechanism is easy to implement in practice, sampling with fixed period will lead to congestion of communication bandwidth and waste of network resources [4–6]. Especially for microprocessors with limited processing resources, it is urgent to establish a more effective communication mechanism to reduce the transmission of redundant data.