一种有效的不确定分数阶T-S模糊系统的控制器设计方法  

An effective method of controller design for uncertain fractional T-S fuzzy systems

作　　者：张雪峰[1] 刘洋洋 ZHANG Xue-feng;LIU Yang-yang(School of Sciences, Northeastern University, Shenyang 110819,China)

机构地区：[1]东北大学理学院

出　　处：《控制与决策》2019年第7期1469-1474,共6页Control and Decision

基　　金：国家自然科学基金项目(61673094,61673100)

摘　　要：考虑分数阶非线性系统的稳定和镇定问题,基于线性矩阵不等式(LMI)方法,对分数阶T-S模糊系统进行研究。利用并行分布补偿法,设计分数阶T-S模糊系统的控制器。考虑阶次满足0 <α<1的分数阶系统,给出可以利用Matlab求解的LMI形式的T-S模糊控制器设计镇定判据。该判据的优点是可以处理具有正实部特征根的分数阶T-S模糊系统的稳定性和镇定问题,能够保持与Matignon分数阶系统稳定性结论的一致性,并克服其他方法只能处理特征根在负实部的方法的局限性和保守性。数值仿真结果验证了所提控制器设计方法的有效性。Considering the stability and stabilization of a class of nonlinear fractional order systems, based on the linear matrix inequality(LMI) approach, fractional order T-S fuzzy systems are studied. Using the method of parallel distributed compensation, controllers of fractional order T-S fuzzy systems are designed. Considering the fractional order T-S fuzzy systems with the order α satisfying 0 <α< 1, stabilization criterion is given in terms of LMI, which can be solved by Matlab. This criterion can handle the problems of the stability and stabilization of fractional order T-S fuzzy systems which have positive real eigenvalues, while maintaining the consistency with the stability criterion of fractional order systems from Matignon. The limitation and conservatsm of the eigenvalues in negative real parts in the other methods are solved. Numerical simulation results verify the effectiveness of the proposed controller design method.

关 键 词：分数阶系统 T-S模糊模型 模糊状态反馈控制器 线性矩阵不等式(LMI) 

分 类 号：TP18[自动化与计算机技术—控制理论与控制工程]