Fuzzy Filtering with Multiple Signal Transmissions

Abstract

This chapter investigates the filtering problem for T–S fuzzy systems, where multiple signals are considered to be transmitted through the communication channel. Firstly, the $\mathcal {l}_2$–$\mathcal {l}_\infty$ filtering problem for T–S fuzzy systems with quantization is proposed, in which the measurement output and the performance output signals of the system are quantized by two static quantizers before being transmitted over the communication channel, respectively. Secondly, the induced $\mathcal {l}_\infty$ filtering problem for T–S fuzzy systems is proposed, in which the measurement output and the performance output are taken into account the data packet dropout phenomenon modeled by two stochastic variables. Sufficient conditions are given to ensure that the filtering error system is not only stochastically stable but also has a prescribed induced $\mathcal {l}_\infty$ performance. Thirdly, the $\mathcal {H}_{\infty }$ filtering problem for the T–S fuzzy systems is proposed, in which the measurement output and the performance output signals of the system are quantized by two dynamic quantizers. And the conditions are given to ensure the filtering error system is asymptotically stable with the prescribed $\mathcal {H}_{\infty }$ performance index. Finally, some examples are given to demonstrate the effectiveness of the proposed filtering methods for T–S fuzzy systems, respectively.