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A Novel Finite-Sum Inequality-Based Method for Robust H∞ Control of Uncertain Discrete-Time Takagi-Sugeno Fuzzy Systems With Interval-Like Time-Varying Delays
IEEE Transactions on Cybernetics ( IF 11.8 ) Pub Date : 2018-09-01 , DOI: 10.1109/tcyb.2017.2743161 Xian-Ming Zhang , Qing-Long Han , Xiaohua Ge
IEEE Transactions on Cybernetics ( IF 11.8 ) Pub Date : 2018-09-01 , DOI: 10.1109/tcyb.2017.2743161 Xian-Ming Zhang , Qing-Long Han , Xiaohua Ge
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.
中文翻译:
一种基于有限和不等式的不确定时滞不确定离散Takagi-Sugeno模糊系统的鲁棒H∞控制方法
本文关注的是鲁棒性问题 $ {H} _ {\ infty} $ 似时变时滞的不确定离散Takagi-Sugeno模糊系统的控制。提出了一种新的基于有限和不等式的方法,可以更精确地估计某些Lyapunov泛函的正向差,从而导致保守性较低。首先,辅助矢量函数用于建立两个有限和不等式,它们可以为出现在Lyapunov函数正向差异中的有限和项产生更严格的边界。其次,采用基于矩阵的二次凸方法等效地将原始矩阵不等式(包括随时间变化的延迟的二次多项式)转换为两个边界矩阵不等式,从而为生成的闭合闭环提供了一个不太保守的有界实数引理(BRL)。循环系统。第三,基于BRL, $ {H} _ {\ infty} $ 推导了模糊控制器。最后,提供了两个数值示例和一个计算机模拟的卡车-拖车系统,以显示所获得结果的有效性。
更新日期:2018-09-01
中文翻译:
一种基于有限和不等式的不确定时滞不确定离散Takagi-Sugeno模糊系统的鲁棒H∞控制方法
本文关注的是鲁棒性问题