Narimani Mohammand, Lam H K, Dilmaghani R, Wolfe Charles
Division of Engineering, King's College London, London, UK.
IEEE Trans Syst Man Cybern B Cybern. 2011 Jun;41(3):713-24. doi: 10.1109/TSMCB.2010.2086443. Epub 2010 Nov 18.
Relaxed linear-matrix-inequality-based stability conditions for fuzzy-model-based control systems with imperfect premise matching are proposed. First, the derivative of the Lyapunov function, containing the product terms of the fuzzy model and fuzzy controller membership functions, is derived. Then, in the partitioned operating domain of the membership functions, the relations between the state variables and the mentioned product terms are represented by approximated polynomials in each subregion. Next, the stability conditions containing the information of all subsystems and the approximated polynomials are derived. In addition, the concept of the S-procedure is utilized to release the conservativeness caused by considering the whole operating region for approximated polynomials. It is shown that the well-known stability conditions can be special cases of the proposed stability conditions. Simulation examples are given to illustrate the validity of the proposed approach.
针对具有不完美前提匹配的基于模糊模型的控制系统，提出了基于松弛线性矩阵不等式的稳定性条件。首先，推导了包含模糊模型和模糊控制器隶属函数乘积项的李雅普诺夫函数的导数。然后，在隶属函数的划分操作域中，状态变量与上述乘积项之间的关系由每个子区域中的近似多项式表示。接下来，推导了包含所有子系统信息和近似多项式的稳定性条件。此外，利用S-过程的概念来消除因考虑近似多项式的整个操作区域而产生的保守性。结果表明，著名的稳定性条件可以是所提出稳定性条件的特殊情况。给出了仿真例子来说明所提方法的有效性。
