Adaptive Event-triggered Dissipative Filtering for Delayed T-S Fuzzy Systems Via Fuzzy Lyapunov Functions

This article is concerned with adaptive event-triggered dissipative filtering for delayed T-S fuzzy systems via fuzzy Lyapunov functions. Firstly, a new event-triggered scheme with an adaptive threshold for delayed T-S fuzzy systems is proposed, and it can alleviate the data transmission burden of communication channels while ensuring the desired control performance. Secondly, the filtering error system is modeled as a delayed T-S fuzzy system by employing the time-delay system modeling method. Thirdly, a suitable augmented Lyapunov functional involving the fuzzy line-integral Lyapunov function is presented. Compared with the existing functions, this augmented Lyapunov functional takes the time derivative information of the membership function into account more fully. By using the Lyapunov method, the asymptotically stability and strictly $(\wp ,\Re ,\mathfrak{H}) - \alpha $ dissipativity of the considered T-S fuzzy system can be ensured. In addition, the adaptive event trigger weight matrix and the suitable dissipative filters can be obtained by solving some linear matrix inequalities(LMIs). Finally, a numerical example is presented to verify the effectiveness of the proposed method.