隶属函数依赖的时变时滞模糊系统的控制  

Membership-function-dependent control of fuzzy systems with time-varying delays

作　　者：周坤 齐淑楠 李靖[2] 靳留乾[3] 蔡继荣[4] 黄天民[5] ZHOU Kun;QI Shu-Nan;LI Jing;JIN Liu-Qian;CAI Ji-Rong;HUANG Tian-Min(College of Mechanical and Electrical Engineering,China Jiliang University,Hangzhou 310018,China;School of Computer Science and Technology,Zhoukou Normal University,Zhoukou 466001,China;School of Business and Management,Chongqing University of Posts and Telecommunications,Chongqing 400065,China;School of Business Planning,Chongqing Technology and Business University,Chongqing 400067,China;School of Mathematics,Southwest Jiaotong University,Chengdu 611756,China)

机构地区：[1]中国计量大学机电工程学院,杭州310018 [2]周口师范学院计算机科学与技术学院,周口466001 [3]重庆邮电大学经济管理学院,重庆400065 [4]重庆工商大学商务策划学院,重庆400067 [5]西南交通大学数学学院,成都611756

出　　处：《四川大学学报（自然科学版）》2019年第4期645-653,共9页Journal of Sichuan University(Natural Science Edition)

基　　金：重庆市社会科学规划项目(2016BS082);国家自然科学基金(61473239,51475391);重庆市前沿与应用基础研究计划项目(cstc2014jcyjA00050)

摘　　要：研究了时变时滞T-S模糊系统的稳定性分析和镇定问题.首先,构造一个增广Lyapunov-Krasovskii函数,结合自由权矩阵不等式,以线性矩阵不等式(LMIs)形式给出了时滞依赖的稳定性准则.基于状态空间分割技术,构造一些由子空间的局部上下确界的凸组合表示的分段隶属函数去近似逼近隶属函数,充分考虑隶属函数的边界信息,同时引入松弛矩阵,进而得到了更为放松的隶属函数依赖的稳定性结果;其次,基于前提不匹配技术,提出了变时滞模糊系统的状态反馈控制器的设计方法,其隶属函数及模糊规则数目可以自由选取,从而提高了控制器设计的灵活性;最后,给出三个仿真实例证明所提方法的有效性.To investigate the stability analysis and stabilization for T-S fuzzy systems with time-varying delays,an augmented Lyapunov-Krasovskii function is first constructed and delay-dependent stability criteria,combining with the free-matrix-based integral inequality,are defined in terms of linear matrix inequalities(LMIs).Based on the state space decomposition method,some piecewise membership functions,which are locally represented in terms of the convex combinations of the supremum and infimum of some local basis functions,are employed to approximate the membership functions,some relaxed membership-function-dependent stability results are obtained with fully consideration of the boundary information of membership functions and introduction of some slack matrices.Secondly,state feedback controllers for the fuzzy systems with time-varying delays are presented based on the imperfect premise matching technique,in which the membership functions and the number of fuzzy rules are allowed to be designed freely,as a result,the flexibility of controller design is then improved.Finally three numerical examples are given to demonstrate the effectiveness of the proposed approaches.

关 键 词：自由权矩阵不等式 状态空间分割 分段隶属函数 隶属函数依赖 前提不匹配 

分 类 号：TP273[自动化与计算机技术—检测技术与自动化装置]