Hankel Norm Model Reduction of Discrete-Time Interval Type-2 T-S Fuzzy Systems With State Delay

被引:9
|
作者
Zeng, Yi [1 ]
Lam, Hak-Keung [1 ]
Wu, Ligang [2 ]
机构
[1] Kings Coll London, Dept Engn, London WC2R 2LS, England
[2] Harbin Inst Technol, Dept Control Sci & Engn, Harbin 150001, Peoples R China
基金
中国国家自然科学基金;
关键词
Reduced order systems; Fuzzy systems; Uncertainty; Delay effects; Mathematical model; Symmetric matrices; Numerical models; Discrete-time systems; Hankel norm; interval type-2 (IT2) Takagi-Sugeno (T– S) fuzzy model; model reduction; state delay; STABILITY ANALYSIS; BALANCED TRUNCATION; VARYING DELAY; LOGIC SYSTEMS; MOBILE ROBOT; DESIGN; APPROXIMATION; OPTIMIZATION; CONTROLLERS;
D O I
10.1109/TFUZZ.2019.2949755
中图分类号
TP18 [人工智能理论];
学科分类号
081104 ; 0812 ; 0835 ; 1405 ;
摘要
This article focuses on the model reduction problem of discrete-time time-delay interval type-2 Takagi-Sugeno (T-S) fuzzy systems. Compared with the type-1 T-S fuzzy system, the interval type-2 T-S fuzzy system has more advantages in expressing nonlinearity and capturing uncertainties. In addition, in order to simplify the analysis process, complex high-order systems can be approximated as low-order systems, which is called model reduction. In previous studies, there are few researches on model reduction of the interval type-2 T-S fuzzy system with time delay. Hankel norm is adopted to limit the error after model reduction. Based on Jensen's inequality, a linear matrix inequality (LMI) condition for the Hankel norm performance of the error system is obtained. A membership-function-dependent method based on piecewise linear membership functions is utilized to deal with mismatched membership functions where information of membership functions will be used for relaxing analysis results. Next, by a convex linearization design, the model reduction problem is formulated as a convex LMI feasibility/optimization condition. Numerical examples are given to verify the validity of the analysis.
引用
收藏
页码:3276 / 3286
页数:11
相关论文
共 50 条
  • [1] Model Reduction of Discrete-Time Interval Type-2 T-S Fuzzy Systems
    Zeng, Yi
    Lam, Hak-Keung
    Wu, Ligang
    [J]. IEEE TRANSACTIONS ON FUZZY SYSTEMS, 2018, 26 (06) : 3545 - 3554
  • [2] Hankel-Norm-Based Model Reduction for Stochastic Discrete-Time Nonlinear Systems in Interval Type-2 T-S Fuzzy Framework
    Zeng, Yi
    Lam, Hak-Keung
    Wu, Ligang
    [J]. IEEE TRANSACTIONS ON CYBERNETICS, 2021, 51 (10) : 4934 - 4943
  • [3] Optimal Model Approximation of Discrete-Time T-S Fuzzy Systems: Hankel Norm Approach
    Peng Tong
    Xiong Yongyang
    Yang Xiaozhan
    Yang Rongni
    Wu Ligang
    [J]. 2013 32ND CHINESE CONTROL CONFERENCE (CCC), 2013, : 39 - 44
  • [4] Delay-dependent stabilization of discrete-time interval type-2 T-S fuzzy systems with time-varying delay
    Zhao, Tao
    Dian, Songyi
    [J]. JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS, 2017, 354 (03): : 1542 - 1567
  • [5] Finite-frequency model reduction of discrete-time T-S fuzzy state-delay systems
    Ding, Da-Wei
    Xie, Xiangpeng
    Du, Xin
    Li, Xiao-Jian
    [J]. NEUROCOMPUTING, 2016, 203 : 121 - 128
  • [6] Model Approximation for Discrete-Time State-Delay Systems in the T-S Fuzzy Framework
    Wu, Ligang
    Su, Xiaojie
    Shi, Peng
    Qiu, Jianbin
    [J]. IEEE TRANSACTIONS ON FUZZY SYSTEMS, 2011, 19 (02) : 366 - 378
  • [7] Stabilization of Interval Type-2 T-S Fuzzy Control Systems with Time Varying Delay
    Yang Feisheng
    Guan Shouping
    [J]. 2013 32ND CHINESE CONTROL CONFERENCE (CCC), 2013, : 3397 - 3401
  • [8] Fault Detection Filtering Design for Discrete-Time Interval Type-2 T-S Fuzzy Systems in Finite Frequency Domain
    Wang, Meng
    Feng, Gang
    Qiu, Jianbin
    Yan, Huaicheng
    Zhang, Hao
    [J]. IEEE TRANSACTIONS ON FUZZY SYSTEMS, 2021, 29 (02) : 213 - 225
  • [9] A new interval type-2 fuzzy controller for stabilization of interval type-2 T-S fuzzy systems
    Zhao, Tao
    Xiao, Jian
    [J]. JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS, 2015, 352 (04): : 1627 - 1648
  • [10] State-Feedback Based Fuzzy Control Design for Discrete-Time Interval Type-2 Fuzzy Bilinear Delay Systems
    Li, Lin
    Li, Jiangrong
    Mao, Chenfei
    [J]. PROCEEDINGS OF THE 39TH CHINESE CONTROL CONFERENCE, 2020, : 2221 - 2226