Lam H K, Seneviratne Lakmal D
Division of Engineering, King's College London, London, UK.
IEEE Trans Syst Man Cybern B Cybern. 2008 Jun;38(3):617-28. doi: 10.1109/TSMCB.2008.915530.
This paper presents the stability analysis of interval type-2 fuzzy-model-based (FMB) control systems. To investigate the system stability, an interval type-2 Takagi-Sugeno (T-S) fuzzy model, which can be regarded as a collection of a number of type-1 T-S fuzzy models, is proposed to represent the nonlinear plant subject to parameter uncertainties. With the lower and upper membership functions, the parameter uncertainties can be effectively captured. Based on the interval type-2 T-S fuzzy model, an interval type-2 fuzzy controller is proposed to close the feedback loop. To facilitate the stability analysis, the information of the footprint of uncertainty is used to develop some membership function conditions, which allow the introduction of slack matrices to handle the parameter uncertainties in the stability analysis. Stability conditions in terms of linear matrix inequalities are derived using a Lyapunov-based approach. Simulation examples are given to illustrate the effectiveness of the proposed interval type-2 FMB control approach.
本文提出了基于区间二型模糊模型（FMB）的控制系统的稳定性分析。为了研究系统稳定性，提出了一种区间二型Takagi-Sugeno（T-S）模糊模型，它可被视为多个一型T-S模糊模型的集合，用于表示存在参数不确定性的非线性对象。通过下限和上限隶属函数，可以有效地捕捉参数不确定性。基于区间二型T-S模糊模型，提出了一种区间二型模糊控制器来闭合反馈回路。为便于进行稳定性分析，利用不确定性足迹信息来制定一些隶属函数条件，这使得在稳定性分析中可以引入松弛矩阵来处理参数不确定性。使用基于李雅普诺夫的方法推导出了基于线性矩阵不等式的稳定性条件。给出了仿真示例以说明所提出的区间二型FMB控制方法的有效性。
