中文摘要：

本文利用Lyapunov方法研究了T-S模糊广义离散系统稳定与镇定问题.针对该系统的开环情况,给出了其渐近稳定的充分条件.在此基础上,设计了模糊状态控制器,给出了该类系统的闭环系统是全局渐近稳定的充分条件,并将此条件用线性矩阵不等式（LMI）表示.最后,引入一种新的受限等价分解,将所考虑的系统分解成两个低维的子系统,设计了准切换面和离散滑模控制律,使得在控制的作用下,系统解的轨迹沿着准切换流形收敛到原点.

英文摘要：

In this paper, the stability and stabilization problem for T-S fuzzy discrete descriptor system is studied by virtue of the Lyapunov＇s method. The sufficient conditions for the asymptotic stability of the open-loop T-S fuzzy discrete descriptor system are given. Based on the conditions, a fuzzy state controller is designed and the sufficient conditions for the asymptotic stability of the closed- loop system composed by the fuzzy state controller and the T-S fuzzy discrete descriptor system are presented. The conditions are further expressed in the form of linear matrix inequality （LMI）. Finally, a new restricted system is developed and the T-S fuzzy discrete descriptor system is decomposed into two lower dimensional subsystems. A switching function can be chosen and a discrete sliding mode controller is designed, which can make the solution trajectory of the system converge to the origin along the switching manifold.