2-D T-S模糊时滞系统状态反馈H∞控制  

State Feedback H∞Control of 2-D T-S Fuzzy Time-delay Systems

作　　者：彭丹[1] 陈莹 PENG Dan;CHEN Ying(School of Science,Yanshan University,Qinhuangdao 066004,China)

机构地区：[1]燕山大学理学院,河北秦皇岛066004

出　　处：《河南科技大学学报（自然科学版）》2022年第6期82-92,99,M0008,共13页Journal of Henan University of Science And Technology:Natural Science

基　　金：国家自然科学基金杰青项目(61825304);河北省省级科技计划基金项目(F2020203037);河北省自然科学基金创新研究群体项目(F2020203013)。

摘　　要：针对Fornasini-Marchesini(FM)模型描述的具有区间时变时滞的二维(2-D)离散模糊系统,研究延迟依赖稳定性和状态反馈H控制问题。首先,选取包含更多时滞信息的双重及三重求和的Lyapunov-Krasovskii函数(LKF)。其次,利用Wirtinger不等式,得到了一种基于线性矩阵不等式(LMI)的延迟依赖稳定性准则,进而给出了保证所研究系统具有给定H性能的状态反馈控制器的设计方法。最后,考虑热过程的实际算例,通过MATLAB工具箱求得增益矩阵,利用仿真图验证所得定理的正确性。The delay-dependent stability and state feedbackHcontrol problems for two-dimensional(2-D)discrete fuzzy systems with interval time-varying delays described by the Fornasini-Marchesini(FM)model were studied.Firstly,the Lyapunov-Krasovskii function(LKF)with double and triple summation containing more delay information was selected.Secondly,a delay-dependent stability criterion based on linear matrix inequality(LMI)was obtained by using Wirtinger inequality.Then,the design method of state feedback controller was given to assure the givenHperformance of the studied system.Finally,a practical example of thermal process was considered,then the gain matrix was obtained by MATLAB toolbox.The correctness of the theorem is verified by simulation diagram.

关 键 词：二维(2-D)系统 模糊系统 状态反馈 H∞控制 

分 类 号：O231.2[理学—运筹学与控制论]