An approach to design stabilizers and observers for a class of multiple-input multiple-output (MIMO) Takagi–Sugeno (T–S) fuzzy models is developed on the basis of local gains and the searching for a set of interpolation functions capable of properly combining the aforementioned local gains. As expected, the existence of such interpolation functions depends on the controllability and observability properties of the overall multivariable T–S fuzzy model. For that reason, practical controllability and observability tests are also proposed for MIMO T–S fuzzy systems. Some numerical simulations are used in order to validate the efficacy of the method. Besides, the results are compared with an approach based on linear matrix inequalities, namely parallel distributed compensation.

中文翻译：

---

基于新插值函数的一类多变量TS模糊模型的稳定器和观测器设计

一种设计稳定器和观测器的方法用于一类多输入多输出 (MIMO) Takagi-Sugeno (T-S) 模糊模型是基于局部增益和搜索一组能够正确计算的插值函数结合上述局部收益。正如预期的那样，这种插值函数的存在取决于整体多变量 T-S 模糊模型的可控性和可观察性。出于这个原因，还建议对 MIMO T-S 模糊系统进行实际的可控性和可观察性测试。为了验证该方法的有效性，使用了一些数值模拟。此外，将结果与基于线性矩阵不等式的方法，即并行分布式补偿进行了比较。