This paper presents a new approach in modeling and control of multi-input multi-output (MIMO) systems that have non-differentiable operating points. A circle criterion is introduced at the non-differentiable operating points to divide the entire operating region into two parts. Takagi-Sugeno fuzzy models are developed in each part, and a switching framework is introduced to model the operating region. Accordingly, a sliding mode controller (SMC) is developed. The proposed modeling and controller are implemented on the benchmark quadruple tank process (QTP). It is demonstrated that the proposed modeling and controller design provides simplicity and universality in a set of nonlinear systems; it is robust with respect to various internal and external disturbances and model uncertainties which allows for accurate regulation and tracking; and it converges in finite time, is capable of controlling nonlinear systems with coupling dynamic, and enables fuzzy modeling of continuous-time systems without imposing differentiability.

中文翻译：

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一类不可微分多输入多输出非线性系统的模糊建模与控制

本文提出了一种对具有不可微分操作点的多输入多输出 (MIMO) 系统进行建模和控制的新方法。在不可微分的操作点处引入圆准则，将整个操作区域分为两部分。每个部分都开发了Takagi-Sugeno模糊模型，并引入了切换框架来对操作区域进行建模。因此，开发了一种滑模控制器（SMC）。所提出的建模和控制器在基准四罐工艺（QTP）上实现。证明了所提出的建模和控制器设计在一组非线性系统中提供了简单性和通用性；它对各种内部和外部干扰和模型不确定性具有鲁棒性，可以进行准确的调节和跟踪；