This paper focuses on the $H_{\infty }$ control problem for a class of discrete-time persistent dwell-time (PDT) switched nonlinear singularly perturbed systems (SPSs) under T–S fuzzy model. In order to make the system more consistent with the actual situation, the signal quantization associated with a logarithmic quantizer and the packet dropouts governed by a Bernoulli variable are considered simultaneously. And, the persistent dwell-time switching mechanism is employed to describe the fast and slow switching among several subsystems in the investigated systems alternatively. Based on the Lyapunov function approach and Takagi–Sugeno (T–S) fuzzy technique, some sufficient conditions are obtained, which can ensure the exponentially mean-square stable (EMSS) and $H_{\infty }$ performance of the closed-loop system. In addition, a unified fuzzy controller design methodology is established for the nonlinear SPSs, so that the fuzzy controller can be designed depending on whether the fast states of the systems are available or not. Finally, a numerical example and a series DC motor model are provided to demonstrate the superiority and practicability of the obtained theoretical results.

本文着重于 $H_{\infty }$T-S模糊模型下一类离散时间持续驻留时间（PDT）切换非线性奇异摄动系统（SPS）的控制问题。为了使系统更符合实际情况，同时考虑了与对数量化器相关的信号量化和由伯努利变量控制的丢包。并且，采用持久驻留时间切换机制来交替描述所研究系统中几个子系统之间的快速和慢速切换。基于Lyapunov函数方法和Takagi-Sugeno（T-S）模糊技术，得到了一些充分条件，可以保证指数均方稳定（EMSS）和$H_{\infty }$闭环系统的性能。此外，针对非线性SPS建立了统一的模糊控制器设计方法，从而可以根据系统的快速状态是否可用来设计模糊控制器。最后，通过数值算例和串联直流电机模型论证了所得理论结果的优越性和实用性。