采用PQLF的不确定模糊系统最优保性能控制

对一类模有界的参数不确定T-S模糊系统的保性能控制问题进行了分析研究。一个二次指标函数表征了闭环系统的性能。采用分段二次Lyapunov函数(Piecewise quadratic Lyapunov function,PQLF)方法,在使闭环系统渐近稳定的前提下以线性矩阵不等式(Linear matrix inequality,LMI)的形式给出了一种鲁棒最优保性能控制律。同时提出了一种新型分段并行补偿(Parallel distributed compensation,PDC)控制策略。该PDC控制器同样反映了模糊系统前提变量的规则结构信息。数值仿真显示,采用该设计方法所得到的闭环保性能值优于传统二次Lyapunov函数(Common quadratic Lyapunov function,CQLF)方法下的闭环保性能值,且系统动态性能良好,鲁棒性强。

Optimal Guaranteed Cost Control for Uncertain Fuzzy Systems Based on Piecewise Quadratic Lyapunov Function

Based on the piecewise quadratic Lyapunov function(PQLF) approach, the optimally guaranteed cost control of a class of continuous Takagi-Sugeno(T-S) fuzzy systems is studied with norm-bounded parametric uncertainties.A linear quadratic cost function is considered as a performance index of closed-loop fuzzy systems.Then,a robust optimally guaranteed cost control law is derived in the form of linear matrix inequality(LMI) by the PQLF approach for stabilization of closed-loop fuzzy systems.A piecewise parallel distributed compensation(PDC) scheme containing the structural information of the rule base is introduced.A numerical example illustrates the efficiencies of the PQLF approach and the PDC stabilization method.The controller designed by the PQLF approach is robust against norm-bounded parametric uncertainties and has better performance than those of the common quadratic Lyapunov function(CQLF) approach.