基于分段模糊Lyapunov函数的模糊系统分析与设计

在分析模糊系统前提规则结构信息的基础上,将模糊Lyapunov函数和分段Lyapunov函数结合,构造出一类连续模糊系统的分段模糊Lyapunov函数。采用并行分配补偿(PDC)结构,利用分段模糊Lyapunov函数进行了稳定性分析与控制律设计,得到了线性矩阵不等式(LMI)形式的连续系统镇定方法。该方法减少了模糊Lyapunov函数与分段Lyapunov函数的局限性,继承两者的优点,所得稳定性判据更为宽松,控制系统具有良好的控制性能。仿真实例表明了该方法的有效性。

Analysis and Design of Fuzzy Systems Based on Piecewise Fuzzy Lyapunov Function

The stability analysis and control law design of a class of continuous fuzzy systems were delt with. By taking advantage of the structure information of the premise rule base, the piecewise fuzzy Lyapunov function was proposed. Based on the piecewise fuzzy Lyapunov function, a control design method for stabilization of continuous fuzzy systems was derived in the format of linear inequality matrix (LMI) by using the parallel distributed compensation (PDC) strategy. This method reduces the conservatism of both piecewise Lyapunov function and fuzzy Lyapunov function. The stability condition obtained is more relaxed and the control system has good performance. The efficiency of the method is illustrated through the simulation of some numerical examples.