This paper presents four sliding mode observers (SMOs) based on a novel approach in Takagi–Sugeno (TS) fuzzy modeling of multi-input multi-output (MIMO) non-linear systems that have non-differentiable operating points. A comprehensive approach is proposed to using the TS fuzzy model (TSFM) in the field of non-differentiable nonlinear systems, where the TSFM is an approximation with high accuracy and a negligible error (2$\epsilon$) of the nonlinear model. Furthermore, the considered system can be with measurable or unmeasurable premise variables. The observers are synthesized for the above two cases and dynamic observers for state estimations of MIMO non-linear Lipschitz systems. The dynamic gain of the observer is established from inspiring state-space representation of an LTI system with error as input, internal states, and the gain of the observer as output. The dynamics used in the gain of the observer will increase the degrees of freedom in the design procedure and a generalization to the one used in previous works. The proposed method is applicable for continuous-time, but not necessarily differentiable, nonlinear systems. Considering the inherent strongly nonlinear and coupling performance of the plant, the switching method driven by states is presented. This paper presents a comparison of four SMOs and multiple-model adaptive estimation (MMAE) for benchmark hydraulic wind power transfer (HWPT). Simulation results demonstrate improvement in the state observation convergence rate and simplicity and universality of the proposed approach.

本文基于Takagi-Sugeno（TS）模糊建模的一种新方法，介绍了四个滑模观测器（SMO），该模型对具有不可微操作点的多输入多输出（MIMO）非线性系统进行了建模。提出了一种在不可微非线性系统领域中使用TS模糊模型（TSFM）的综合方法，其中TSFM是高精度且近似值可忽略不计的近似值（2$\epsilon$）的非线性模型。此外，所考虑的系统可以具有可测量或不可测量的前提变量。对于上述两种情况，观测器被合成，并且对于MIMO非线性Lipschitz系统的状态估计，动态观测器被合成。观察者的动态增益是通过激励LTI系统的状态空间表示而建立的，其中误差作为输入，内部状态以及观察者的增益作为输出。观察者的增益所使用的动力学将增加设计过程中的自由度，并将其推广到以前的作品中。所提出的方法适用于连续时间但不一定可微的非线性系统。考虑到设备固有的强非线性和耦合性能，提出了状态驱动的切换方法。本文对基准水力风力发电（HWPT）的四种SMO和多模型自适应估计（MMAE）进行了比较。仿真结果证明了状态观测收敛速度的提高以及所提方法的简单性和通用性。