摘要
研究一类含有状态时滞和输入时滞的T-S模糊系统的稳定性分析和镇定问题.首先,构造一个含三重积分的Lyapunov-Krasovskii(L-K)泛函,利用一个近期提出的二重积分不等式和基于辅助函数的积分不等式处理积分项.为了得到更为放松的时滞依赖的稳定性结果,考虑隶属度函数的边界信息,选择分段隶属函数去近似隶属度函数,同时引入松弛矩阵,以线性矩阵不等式(LMIs)形式给出保守性较小的隶属函数依赖的稳定性准则;然后,基于前提不匹配技术,结合Finsler引理,首次提出含状态和输入时滞的模糊系统的状态反馈控制器的设计方法,该模糊控制器不要求与模糊系统拥有相同的隶属度函数和模糊规则数目,从而提高设计的灵活性;最后,通过给出3个仿真算例表明所提出方法的先进性和有效性.
This paper focuses on the stability analysis and stabilization for a class of T-S fuzzy systems with state and input delays. Firstly, a Lyapunov-Krasovskii (L-K) functional with triangle integral is constructed, and a recently developed double integral inequality and the auxiliary function-based integral inequality are selected to deal with the integral term in the derivative of the Lyapunov-Krasovskii functional. In order to obtain further relaxed delay-dependent stability results, the boundary information on membership functions is considered, the piecewise membership functions are employed to approximate the membership functions, meanwhile, some slack matrices are employed, and relaxed membership-function-dependent stability criteria are obtained in terms of linear matrix inequalities (LMIs). Then, under the imperfect premise matching technique, combining with the Finsler lemma, a fuzzy state feedback control design method is presented for the first time for the T-S fuzzy systems with state and input delays. The fuzzy controller is required to employ the same premise membership functions and the number of fuzzy rules as the fuzzy model, and then the flexibility of controller design is improved. Finally, three numerical examples are given to illustrate progressiveness and effectiveness of the presented approach.
作者
周坤
齐淑楠
黄天民
赵涛
ZHOU Kun;QI Shu-nan;HUANG Tian-min;ZHAO Tao(School of Electrical Engineering,Southwest Jiaotong University,Chengdu 610031,China;School of Computer Science and Technology, Zhoukou Normal University,Zhoukou 466001,China;School of Mathematics,Southwest Jiaotong University,Chengdu 611756,China;School of Electrical Engineering and Information,Sichuan University,Chengdu 610065,China)
出处
《控制与决策》
EI
CSCD
北大核心
2019年第9期1819-1830,共12页
Control and Decision
基金
国家自然科学基金项目(61473239,51475391)
关键词
积分不等式
时滞依赖
分段隶属函数
隶属函数依赖
前提不匹配技术
Finsler引理
integral inequality
delay-dependent
piecewise membership functions
membership-function-dependent
imperfect premise matching technique
Finsler lemma
