T-S模糊广义系统稳定性分析及控制器设计

Design of controller forT-S fuzzy descriptor systems

针对T-S模糊离散广义系统稳定性判别条件严格,不具备更好适用性等问题,提出一种优化判据的新方法。该方法利用模糊Lyapunov函数分析了T-S模糊离散广义系统的稳定性问题,经过推导得出了更具一般性的稳定充分条件,并对得到的结论予以严格的数学证明;基于并行分布补偿(PDC)设计了模糊控制器,在原有T-S模糊模型的基础上,引入了Lyapunov函数,然后根据稳定性判别表达式不同的处理方式,提出了更宽松的T-S模糊离散广义系统稳定性判别条件,并对推论进行了证明。对T-S模糊离散广义系统的稳定性问题的优化,使得模糊离散广义系统具有更好的通用性,更贴近实际及更稳定的控制作用。

In view of the fact that the stability criterion of T-S fuzzy discrete descriptor system is very rigid, so its application is somehow difficult. A new method of optimal stability criterion is put forward. The stability of T-S fuzzy discrete descriptor system is studied using fuzzy Lyapunov function, and a new stability condition is derived through rigid mathematic operation. The fuzzy controller is designed on the basis of parallel distributed compensations （PDC） in order to obtain an improved algorithm. Introducing Lyapunov function makes the criterion condition more generous, thus, the new T-S fuzzy descriptor system is more universal, more practical, and more stable than the traditional controller.