引用本文:张雪峰,艾洁,赵泽丽.不确定非方广义分数阶T–S模糊系统的鲁棒镇定[J].控制理论与应用,2023,40(1):47~54.[点击复制]
ZHANG Xue-feng,AI Jie,ZHAO Ze-li.Robust stabilization for uncertain rectangular descriptor fractional order T–S fuzzy systems[J].Control Theory and Technology,2023,40(1):47~54.[点击复制]
不确定非方广义分数阶T–S模糊系统的鲁棒镇定
Robust stabilization for uncertain rectangular descriptor fractional order T–S fuzzy systems
摘要点击 770  全文点击 303  投稿时间：2021-06-05  修订日期：2022-04-20
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DOI编号  10.7641/CTA.2021.10486
  2023,40(1):47-54
中文关键词  非方广义分数阶系统  T–S模糊模型  动态补偿器  鲁棒镇定  线性矩阵不等式
英文关键词  rectangular descriptor fractional order systems  T–S fuzzy model  dynamic compensator  robust stabilization  linear matrix inequalities
基金项目  国家重点研发计划项目(2020YFB1710003), 国家自然科学基金项目(U20A20189), 辽宁省振兴人才计划项目(XLYC1907049)资助.
作者单位E-mail
张雪峰* 东北大学理学院 zhangxuefeng@mail.neu.edu.cn 
艾洁 东北大学理学院  
赵泽丽 东北大学信息科学与工程学院  
中文摘要
      针对不确定非方广义分数阶T–S模糊系统阶数为0 < α < 1的鲁棒镇定问题, 提出了一个有效的判据. 首先, 利用一个新的T–S模糊动态补偿器, 将不确定非方广义分数阶T–S模糊系统转化为一个增广的不确定方形广义分数 阶T–S模糊系统. 由于增广变量的引入, 动态补偿器的设计问题可以等价为静态输出反馈控制器的设计问题. 其次, 设计一个分数阶导数反馈控制器对得到的增广系统进行正常化处理. 然后, 对正常化得到的不确定分数阶T–S模糊 系统进行研究, 得到一个系统渐近稳定的充分条件. 该条件保守性小并且形式简洁. 最后, 通过一个数值算例和一个 实际例子验证了本文所提出结论的正确性和有效性.
英文摘要
      An effective criterion is proposed for the robust stabilization for uncertain rectangular descriptor fractional order Takagi-Sugeno (T–S) fuzzy systems with 0 < α < 1. Firstly, by using a new T–S fuzzy dynamic compensator, the uncertain rectangular descriptor fractional order T–S fuzzy systems are transformed into the augmented uncertain square descriptor fractional order T–S fuzzy systems. Due to the introduction of the augmented plant, the gain matrices of the dynamic compensator can be solved by an equivalent static output feedback. Secondly, a fractional order derivative state feedback controller is constructed to normalize the augmented uncertain square descriptor fractional order T–S fuzzy systems. Thirdly, a sufficient condition of asymptotical stability is proposed for normalized systems, which have less conservatism and more concise form. Finally, a numerical example and a practical example are given to verify the effectiveness of the main result in this paper.