This paper deals with the nonfragile $H_\infty$ control problem for a class of discrete-time Takagi–Sugeno fuzzy systems with both randomly occurring gain variations (ROGVs) and channel fadings. The system measurement is subject to fading channels described by Rice fading model where the channel coefficients are random variables taking values within given intervals. The gain matrices of the output feedback controllers are subject to random fluctuations referred to as the ROGVs. The purpose of the addressed problem is to design a parameter-dependent nonfragile output-feedback controller such that, in the presence of both ROGVs and channel fadings, the closed-loop system is exponentially mean-square stable while achieving the guaranteed $H_\infty$ disturbance attenuation level. A gain-scheduling approach is developed to tackle the addressed problem where the designed controller gains are dependent on certain parameters of practical significance (e.g., packet dropout rate). Through stochastic analysis and Lyapunov functional approach, sufficient conditions are derived for the existence of the desired output feedback controller ensuring both the exponential mean-square stability and the prescribed $H_\infty$ performance. The explicit expression of the feedback controller is also characterized by using a semidefinite programming method. Finally, an illustrative example is given to show the usefulness and effectiveness of the proposed design method.

中文翻译：

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受衰落信道影响的非脆弱H无穷大模糊控制的增益调度方法

这篇论文是关于非脆弱的 $H_\infty$ 一类具有随机发生的增益变化 (ROGV) 和信道衰落的离散时间 Takagi-Sugeno 模糊系统的控制问题。系统测量受到莱斯衰落模型描述的衰落信道的影响，其中信道系数是在给定间隔内取值的随机变量。输出反馈控制器的增益矩阵会受到称为 ROGV 的随机波动的影响。解决问题的目的是设计一个参数相关的非脆弱输出反馈控制器，使得在 ROGV 和信道衰落都存在的情况下，闭环系统是指数均方稳定的，同时实现有保证的$H_\infty$干扰衰减水平。开发了一种增益调度方法来解决所解决的问题，其中设计的控制器增益取决于具有实际意义的某些参数（例如，数据包丢失率）。通过随机分析和李雅普诺夫泛函方法，推导出所需输出反馈控制器存在的充分条件，确保指数均方稳定性和规定的$H_\infty$表现。反馈控制器的显式表达式还具有使用半定规划方法的特点。最后，给出了一个说明性的例子来说明所提出的设计方法的有用性和有效性。