Robust H_∞ control based on fuzzy hyperbolic model with time-delay  

作　　者：YizhongWang Huaguang Zhang Xinrui Liu 

机构地区：[1]School of Information Science and Engineering, Northeastern University, Shenyang 110004, China [2]Department of Basic Courses, Shandong University of Science and Technology, Tai＇an 271021, China

出　　处：《Progress in Natural Science:Materials International》2008年第11期1429-1435,共7页自然科学进展·国际材料（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant Nos.60534010,60572070 and 60774048);the Funds for Creative Research Groups of China(Grant No.60325311);the Program for Changjiang Scholars and Innovative Research Team in University(Grant No.IRT0421)

摘　　要：This paper investigates the problems of robust stabilization and robust H∞ control for the fuzzy hyperbolic model （FHM） with time-varying delay. A kind of novel Lyapunov-Krasovskii functional is constructed. By using the descriptor model transformation and free-weighting matrix technique, new delay-dependent sufficient conditions for the existence of desired FHM controllers are devel- oped in terms of linear matrix inequality （LMI）. The designed controllers not only ensure that the closed-loop system is asymptotically stable, but also satisfy a prescribed H∞ performance level. The matrices of the Lyapunov-Krasovskii functional are not required to be diagonally positive-definite. In addition, the traditional restriction that the derivative of the time-varying delay is strictly smaller than one is not needed. Therefore, the obtained results are less conservative. Finally, a simulation example is provided to show the effectiveness of the proposed methods.这篇论文与变化时间的延期为模糊夸张模型(FHM ) 调查柔韧的稳定和柔韧的 H ∞控制的问题。一种新奇 Lyapunov Krasovskii 功能被构造。由使用描述符模型转变和免费重量的矩阵技术，新延期依赖者为需要的 FHM 控制器的存在的足够的条件以线性矩阵不平等(LMI ) 被开发。设计控制器不仅保证靠近环的系统是 asymptotically 稳定的，而且满足规定 H ∞表演水平。Lyapunov Krasovskii 的矩阵功能没被要求斜积极明确。另外，变化时间的延期的衍生物严格地比一个小的传统的限制不被需要。因此，获得的结果是不太保守的。最后，一个模拟例子被提供显示出建议方法的有效性。

关 键 词：Robust H∞ control Fuzzy hyperbolic model （FHM） DELAY Linear matrix inequality 

分 类 号：TP273[自动化与计算机技术—检测技术与自动化装置] O231[自动化与计算机技术—控制科学与工程]