IEEE Trans Cybern. 2018 Sep;48(9):2569-2582. doi: 10.1109/TCYB.2017.2743161. Epub 2017 Sep 22.
This paper is concerned with the problem of robust ${H}{\infty}$ control of an uncertain discrete-time Takagi-Sugeno fuzzy system with an interval-like time-varying delay. A novel finite-sum inequality-based method is proposed to provide a tighter estimation on the forward difference of certain Lyapunov functional, leading to a less conservative result. First, an auxiliary vector function is used to establish two finite-sum inequalities, which can produce tighter bounds for the finite-sum terms appearing in the forward difference of the Lyapunov functional. Second, a matrix-based quadratic convex approach is employed to equivalently convert the original matrix inequality including a quadratic polynomial on the time-varying delay into two boundary matrix inequalities, which delivers a less conservative bounded real lemma (BRL) for the resultant closed-loop system. Third, based on the BRL, a novel sufficient condition on the existence of suitable robust ${H}{\infty}$ fuzzy controllers is derived. Finally, two numerical examples and a computer-simulated truck-trailer system are provided to show the effectiveness of the obtained results.
本文研究了一类具有区间时变时滞的不确定离散时间 Takagi-Sugeno 模糊系统的鲁棒 $H_\infty$ 控制问题。提出了一种基于新的有限和不等式的方法，对某些李雅普诺夫函数的前向差分进行更紧的估计，从而得到更保守的结果。首先，利用辅助向量函数建立了两个有限和不等式，可以对李雅普诺夫函数前向差分中出现的有限和项进行更紧的约束。其次，采用基于矩阵的二次凸方法将包含时变时滞的二次多项式的原始矩阵不等式转化为两个边界矩阵不等式，为所得闭环系统提供了一个更保守的有界实引理 (BRL)。第三，基于 BRL，推导出存在合适的鲁棒 $H_\infty$ 模糊控制器的新充分条件。最后，通过两个数值例子和一个计算机模拟的卡车拖车系统，验证了所得到的结果的有效性。
