Analysis and design of an affine fuzzy system via bilinear matrix inequality
Analysis and design of an affine fuzzy system via bilinear matrix inequality
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DOI：
10.1109/tfuzz.2004.836074
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发表时间：
2005-02
影响因子：
11.9
通讯作者：
Euntai Kim;Chang-Hoon Lee;Youngwan Cho
中科院分区：
文献类型：
--
作者：
Euntai Kim;Chang-Hoon Lee;Youngwan Cho
提出了一种新的仿射模糊系统的分析与设计方法。连续时间和离散时间的情况下被认为是。推导了仿射模糊系统的二次稳定性和可镇定性条件，并将其表示为双线性矩阵不等式。引入两种仿射状态变换（一种是线性的，另一种是非线性的），将被控对象转化为更易处理的仿射形式。这种转换使得仿射模糊系统的稳定性和可镇定性问题成为凸的，并使得这些问题可以用凸线性矩阵不等式（LMI）技术直接求解。模糊控制器的偏置项与增益同时求解。最后通过算例和计算机仿真验证了该方法的适用性。
A novel analysis and design method for affine fuzzy systems is proposed. Both continuous-time and discrete-time cases are considered. The quadratic stability and stabilizability conditions of the affine fuzzy systems are derived and they are represented in the formulation of bilinear matrix inequalities (BMIs). Two diffeomorphic state transformations (one is linear and the other is nonlinear) are introduced to convert the plant into more tractable affine form. The conversion makes the stability and stabilizability problems of the affine fuzzy systems convex and makes the problems solvable directly by the convex linear matrix inequality (LMI) technique. The bias terms of the fuzzy controller are solved simultaneously together with the gains. Finally, the applicability of the suggested method is demonstrated via an example and computer simulation.