中文摘要：

在控制系统中,不仅要求系统能够保持稳定,还要求系统能够满足一定的性能指标,由于T-S模型可以有效的描述许多非线性系统,所以采用带有状态不确定项的T-S模糊系统对控制系统进行描述,又由于被控量的时滞现象大量存在于系统中,所以通过设计有记忆模糊状态反馈控制器,实现系统的保性能控制,同时找到保性能函数的一个上界.首先,通过构造李雅普诺夫（Lyapunov）二-次函数,根据李雅普诺夫（Lyapunov）稳定性理论,证明在此有记忆模糊状态反馈控制器下,对于T-S模糊系统中含有的所有不确定项,形成的闭环系统是渐近稳定的,同时找到保性能函数的一个上界;其次,通过利用线性矩阵不等式（LMI）技术,应用Matlab中的LMI工具箱求解出有记忆状态反馈控制器的反馈增益矩阵;最后,通过仿真算例说明方法的有效性.

英文摘要：

In control systems, the systems are not only required to remain stable but should satisfy certain performance indies. As the T-S model could describe many nonlinear systems effectively, the T-S model with the state uncertainty can describe the control systems. Many delay phenomena of the controller exist in the systems so the memory fuzzy feedback controller is designed to achieve guaranteed cost control of the system and obtain an upper-bound for the given guaranteed cost control. Firstly, by constructing a Lyapunov function and based on the Lyapunov stability theory, it is proved that the closed--loop system is asymptotically stable for all uncertainty in the systems through the application of this memory fuzzy feedback controller and an upper-bound for the given guaranteed cost control is acquired. Secondly, by using the linear matrix inequality （LMI） technique in MATLAB, the feedback controller gain would be found out. Finally, the simulation example is given to illustrate the validity of the proposed method.