In this article, the stability analysis and control synthesis of interval type-2 (IT2) polynomial-fuzzy-model-based networked control systems are investigated under the event-triggered control framework. The nonlinear dynamics in the plant is efficiently represented by an IT2 polynomial fuzzy model that the IT2 membership functions are utilized to capture the uncertainties in the plant. An event-triggered IT2 polynomial fuzzy controller is then designed to stabilize the nonlinear model subject to uncertainties. The stability conditions of the closed-loop control system are summarized in the form of sum-of-squares. Under the imperfectly premise matching (IPM) concept, the membership-function-dependent (MFD) approach is applied to endow the polynomial fuzzy controllers with more flexibility in terms of number of rules and premise membership functions. In the MFD approach under the IPM concept, both the number of rules and the shape of membership functions in the fuzzy models and controllers can be different. Also, the information of IT2 membership functions of the polynomial fuzzy model and controller is considered and adopted to further relax the stability conditions. Furthermore, the intrinsic mismatched issue of the premise variables of the fuzzy model and controllers due to the event-triggering mechanism is handled by the MFD approach. A detailed simulation example is provided to verify the effectiveness of the proposed event-based control strategy.

中文翻译：

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基于事件触发区间2型多项式模糊模型的网络控制系统的隶属函数相关镇定


本文研究了事件触发控制框架下基于区间2型（IT2）多项式模糊模型的网络控制系统的稳定性分析和控制综合。工厂中的非线性动态由 IT2 多项式模糊模型有效地表示，IT2 隶属函数用于捕获工厂中的不确定性。然后设计事件触发的 IT2 多项式模糊控制器来稳定受不确定性影响的非线性模型。闭环控制系统的稳定性条件以平方和的形式概括。在不完全前提匹配（IPM）概念下，应用隶属函数相关（MFD）方法使多项式模糊控制器在规则数量和前提隶属函数方面具有更大的灵活性。在IPM概念下的MFD方法中，模糊模型和控制器中的规则数量和隶属函数的形状都可以不同。此外，还考虑并采用多项式模糊模型和控制器的IT2隶属函数信息来进一步放宽稳定性条件。此外，MFD方法还解决了由于事件触发机制而导致的模糊模型和控制器的前提变量的内在不匹配问题。提供了详细的仿真示例来验证所提出的基于事件的控制策略的有效性。