This paper addresses the model reduction problem of discrete-time interval type-2 (IT2) Takagi_Sugeno (T_S) fuzzy systems, which represent the discrete-time nonlinear systems subject to uncertainty. With the use of IT2 fuzzy sets, the uncertainty of the discrete-time nonlinear system can be captured by the lower and upper membership functions. For a given high-order discrete-time IT2 T_S fuzzy system, the purpose is to find a lower dimensional system to approximate the original system. To achieve the approximation performance, an H∞\mathcal {H}_\infty norm is used to suppress the error between the original system and its simplified system. By introducing a membership-functions-dependent technique and applying a convex linearization method, a membership-functions-dependent condition, which takes the information of membership functions into account, is obtained to reduce the dimensions of system matrices and the number of fuzzy rules of the system. All the obtained theorems are represented as in the form of linear matrix inequalities. Finally, simulation results are demonstrated to show the effectiveness of the derived results.

中文翻译：

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离散时间间隔2型T__模糊系统的模型约简


本文解决了离散时间间隔类型 2 (IT2) Takagi_Sugeno (T_S) 模糊系统的模型简化问题，该系统代表受不确定性影响的离散时间非线性系统。通过使用IT2模糊集，离散时间非线性系统的不确定性可以通过下隶属函数和上隶属函数来捕获。对于给定的高阶离散时间IT2 T_S模糊系统，目的是找到一个较低维的系统来逼近原系统。为了实现近似性能，使用 H∞\mathcal {H}_\infty 范数来抑制原始系统与其简化系统之间的误差。通过引入隶属函数相关技术并应用凸线性化方法，得到了考虑隶属函数信息的隶属函数相关条件，以减少系统矩阵的维数和模糊规则的数量。系统。所有获得的定理都以线性矩阵不等式的形式表示。最后对仿真结果进行了论证，证明了推导结果的有效性。