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

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

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.