IEEE Trans Cybern. 2017 May;47(5):1147-1156. doi: 10.1109/TCYB.2016.2538464. Epub 2016 Apr 5.
This paper investigates the problem of stability analysis and stabilization for Takagi-Sugeno (T-S) fuzzy systems with time-varying delay. By using appropriately chosen Lyapunov-Krasovskii functional, together with the reciprocally convex a new sufficient stability condition with the idea of delay partitioning approach is proposed for the delayed T-S fuzzy systems, which significantly reduces conservatism as compared with the existing results. On the basis of the obtained stability condition, the state-feedback fuzzy controller via parallel distributed compensation law is developed for the resulting fuzzy delayed systems. Furthermore, the parameters of the proposed fuzzy controller are derived in terms of linear matrix inequalities, which can be easily obtained by the optimization techniques. Finally, three examples (one of them is the benchmark inverted pendulum) are used to verify and illustrate the effectiveness of the proposed technique.
本文研究了时变时滞 Takagi-Sugeno（T-S）模糊系统的稳定性分析和镇定问题。通过适当选择 Lyapunov-Krasovskii 泛函，并利用时滞分区方法的互凸思想，提出了一种新的时滞 T-S 模糊系统的充分稳定性条件，与现有结果相比，显著降低了保守性。基于所得到的稳定性条件，为所得到的模糊时滞系统设计了基于并行分布补偿律的状态反馈模糊控制器。此外，通过线性矩阵不等式给出了所提出的模糊控制器的参数，这些参数可以通过优化技术很容易地得到。最后，通过三个实例（其中一个是基准倒立摆）来验证和说明所提出方法的有效性。
