离散模糊系统分析与设计的模糊Lyapunov方法

Analysis and Design of Discrete Fuzzy System with Fuzzy Lyapunov Approach

研究离散T-S模糊控制系统基于模糊Lyapunov函数的稳定性分析及控制器设计问题.首先,构造出离散型模糊Lyapunov函数,模糊Lyapunov函数是系数与T-S模糊系统的模糊规则权重相对应的复合型Lyapunov函数.然后,得到了开环系统新的稳定性充分条件,与公共Lyapunov方法的结果相比,这一条件更为宽松.进而,基于一系列线性矩阵不等式设计出模糊控制器.最后,仿真实例说明了该方法的算法和本文条件的优越性.

The stability analysis and fuzzy controller design problem of discrete T-S fuzzy control system are discussed based on fuzzy Lyapunov function. First, a new Lyapunov function for discrete T-S fuzzy system is constructed. The fuzzy Lyapunov function shares the same membership functions with the T-S fuzzy model. Then, a new sufficient condition for the stability of the open-loop system is proposed. This condition is less conservative than the results obtained with the common Lyapunov approach. In addition, the fuzzy controller is designed based on a series of LMIs. At last, simulation example shows the design procedure and the advantage of the proposed method.