Stability Analysis and Performance Design for Fuzzy-Model-Based Control System Under Imperfect Premise Matching
Stability Analysis and Performance Design for Fuzzy-Model-Based Control System Under Imperfect Premise Matching
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DOI：
10.1109/tfuzz.2008.928600
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发表时间：
2009-08
影响因子：
11.9
通讯作者：
H. Lam;M. Narimani
中科院分区：
文献类型：
--
作者：
H. Lam;M. Narimani
本文研究非线性系统的稳定性分析和性能设计。为了便于稳定性分析，Takagi-Sugeno（T-S）模糊模型被用来表示非线性对象。针对T-S模糊模型与模糊控制器不具有相同隶属度函数的不完全匹配前提，提出了一种具有设计灵活性和鲁棒性的模糊控制器，用于控制非线性对象。然而，完美前提匹配所给出的良好特征（导致保守稳定性条件）消失了。本文在不完全匹配的前提下，考虑了模糊模型和控制器的隶属度函数信息。通过引入松弛矩阵，利用基于Lyapunov的方法，得到了基于松弛线性矩阵不等式（LMI）的稳定性条件。此外，基于LMI的性能条件，以保证系统的性能。最后通过仿真实例验证了该方法的有效性。
This paper investigates the stability analysis and performance design of nonlinear systems. To facilitate the stability analysis, the Takagi-Sugeno (T-S) fuzzy model is employed to represent the nonlinear plant. Under the imperfect premise matching in which T-S fuzzy model and fuzzy controller do not share the same membership functions, a fuzzy controller with enhanced design flexibility and robustness property is proposed to control the nonlinear plant. However, the nice characteristic given by the perfect premise matching, leading to conservative stability conditions, vanishes. In this paper, under the imperfect premise matching, information of membership functions of the fuzzy model and controller are considered in stability analysis. With the introduction of slack matrices, relaxed linear matrix inequality (LMI)-based stability conditions are derived using Lyapunov-based approach. Furthermore, LMI-based performance conditions are provided to guarantee system performance. Simulation examples are given to illustrate the effectiveness of the proposed approach.