A staircase membership functions-based H∞control method was proposed for discrete T-S fuzzy control systems. In order to increase the flexibility of controller design, a fuzzy Lyapunov function was im-plemented as the candidate of Lyapunov function. And the non-parallel distributed compensation control-ler was used to close the control loop. Furthermore, staircase membership functions were used to approxi-mate the membership functions of discrete T-S fuzzy model. Due to the discreteness and finiteness of the values of staircase membership functions, the fuzzy matrix inequalities which describe the stability and performance of the closed-loop system can be converted to some linear matrix inequalities. Since the in-formation of membership functions was introduced into the controller design, the conservative of the con-troller design was reduced. Compared with traditional H∞control methods, the presented method could design a fuzzy controller with lower H∞index. A numerical simulation example was given to show the ef-fectiveness of the proposed method.%针对离散T-S模糊控制系统,提出了一种基于阶梯隶属度函数的H∞控制器设计方法.为了增加控制器设计的自由度,采用模糊Lyapunov函数作为候选Lyapunov函数,并利用非并行补偿控制器进行闭环控制. 进一步利用阶梯隶属度函数逼近T-S模糊模型的隶属度函数,根据阶梯隶属度函数取值的离散性和有限性,描述闭环系统稳定性和性能的模糊矩阵不等式可以被转换为若干线性矩阵不等式. 由于隶属度函数的信息被引入到控制器设计之中,降低了控制器设计的保守程度. 相比于传统的H∞控制方法,所提出的方法能够设计出具有更小H∞性能指标的模糊控制器. 给出了一个数值仿真示例验证了方法的有效性.
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