模糊广义离散系统的稳定与镇定  

Stability and Stabilization of T-S Fuzzy Discrete Descriptor Systems

作　　者：梁家荣[1] 张晶华[2] 杜富[2] 

机构地区：[1]广西大学计算机与电子信息学院,南宁530004 [2]广西大学数学与信息科学学院,南宁530004

出　　处：《工程数学学报》2011年第4期435-445,共11页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(61064002);教育部新世纪优秀人才支持计划(NCET-06-0756);广西研究生创新计划项目(105931003061)~~

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.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.

关 键 词：T-S模糊广义离散系统 隶属函数 切换平面 滑模控制 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程]