Induced $\mathcal {L}_\infty$ Quantized Sampled-Data Control for T–S Fuzzy System With Bandwidth Constraint

This article proposes an induced $\mathcal {L}_\infty$ sampled-data control problem for the Takagi–Sugeno (T–S) fuzzy system with dynamic quantization, in which the communication channel is assumed to be bandwidth-constrained. First, according to the input delay approach, the dynamics of the considered closed-loop system is modeled by a delay system with constrained nonlinear term. Then, for the bandwidth-constrained communication channel, a constraint condition is introduced to ensure that the adjustable parameter of the dynamic quantization strategy is limited by a bounding region. The main purpose of the problem addressed is to design a controller, such that the closed-loop system guarantees the asymptotic stability with an induced $\mathcal {L}_\infty$ performance index. The sufficient conditions of stability with induced $\mathcal {L}_\infty$ control performance are given as the basis of controller design. Furthermore, the induced $\mathcal {L}_\infty$ sampled-data control scheme and the improved updating rule of dynamic parameter are proposed. Finally, an example shows the effectiveness of the the proposed controller design scheme.