IEEE Trans Cybern. 2014 Dec;44(12):2784-91. doi: 10.1109/TCYB.2014.2316491. Epub 2014 Apr 29.
This paper is concerned with further studies on control synthesis of discrete-time Takagi-Sugeno (T-S) fuzzy systems. To do this, a novel slack variable technique, which is homogenous polynomially parameter-dependent on both the current-time normalized fuzzy weighting functions and the past-time normalized fuzzy weighting functions with arbitrary degrees, is presented by developing an efficient augmented multi-indexed matrix approach. Under the framework of homogenous matrix polynomials, the algebraic properties of both the current-time normalized fuzzy weighting functions and the past-time normalized fuzzy weighting functions are collected into sets of augmented multi-indexed matrices. Thus, more information about the underlying normalized fuzzy weighting functions is involved into control synthesis. Consequently, the relaxation quality of control synthesis of discrete-time T-S fuzzy systems is improved significantly. Finally, a numerical example is provided to illustrate the effectiveness of the proposed method.
本文致力于进一步研究离散时间 Takagi-Sugeno（T-S）模糊系统的控制综合。为此，通过开发一种有效的增广多索引矩阵方法，提出了一种新的时变松弛变量技术，该技术在任意阶下对当前时间归一化模糊权函数和过去时间归一化模糊权函数是同次多项式参数依赖的。在齐次矩阵多项式的框架下，当前时间归一化模糊权函数和过去时间归一化模糊权函数的代数性质被收集到增广多索引矩阵的集合中。因此，控制综合中包含了更多关于基础归一化模糊权函数的信息。结果，离散时间 T-S 模糊系统的控制综合松弛质量得到了显著提高。最后，通过一个数值例子说明了所提出方法的有效性。
