In this paper, we investigate the stability and performance of the interval type-2 (IT2) polynomial fuzzy-model-based tracking control system, formed by an IT2 polynomial fuzzy model and an IT2 polynomial fuzzy controller, based on the output feedback and sampled-data structure. IT2 fuzzy sets are employed to capture the uncertainties of the nonlinear plant. Furthermore, considering the digital implementation of control strategy and only the system outputs are available, the IT2 polynomial fuzzy controller is of discrete time and output-feedback type. Both membership-function-independent and membership-function-dependent stability analysis, with the consideration of H∞H_\infty performance index, are conducted to develop stability conditions in terms of sum-of-square based on Lyapunov stability theory. The information of membership functions, system states, and sampling process are included in the stability analysis for the relaxation of stability conditions. Simulation examples are presented to verify the effectiveness of the proposed tracking control approach.

中文翻译：

---

区间2型多项式模糊系统的采样数据输出反馈跟踪控制


在本文中，我们研究了基于区间2型（IT2）多项式模糊模型的跟踪控制系统的稳定性和性能，该系统由IT2多项式模糊模型和IT2多项式模糊控制器组成，基于输出反馈和采样-数据结构。 IT2 模糊集用于捕获非线性对象的不确定性。此外，考虑到控制策略的数字实现以及只有系统输出可用，IT2多项式模糊控制器是离散时间和输出反馈型的。考虑到 H∞H_\infty 性能指标，进行与隶属函数无关和与隶属函数相关的稳定性分析，以根据李雅普诺夫稳定性理论制定平方和的稳定性条件。稳定性分析中包含隶属函数、系统状态和采样过程等信息，以放宽稳定性条件。仿真例子验证了所提出的跟踪控制方法的有效性。