一类非线性系统的模糊可靠H_2/H_∞混合控制器设计的LMI方法

LMI-based reliable mixed H_2/H_∞ controller designs for T-S fuzzy systems

基于T-S模糊模型,利用线性矩阵不等式(LMI)方法,研究一类非线性系统的模糊可靠H2/H∞混合控制器设计问题.首先,分别以LMI形式给出了系统模糊可靠H2及H∞控制器存在的充分条件和控制器设计方法;然后,给出系统混合H2/H∞性能的可靠控制器设计方法,所设计的控制器使得故障闭环系统二次稳定,同时满足H∞性能,且优化系统的H2性能指标;最后,通过数值例子验证了结论的正确性和控制器设计方法的有效性.

The problem of reliable mixed H2/H∞ controller for nonlinear systems is discussed by using linear matrix inequality （LMI） approach based on the T-S fuzzy model. Sufficient conditions for H2 and H∞ controllers are given in terms of LMI respectively, and the design methods of reliable H2 and H∞ controller are proposed. The design approach of reliable controller with mixed H2/H∞, performance is given. The designed controller makes the resultant fault closed-loop systems quadratic stable, satisfying the H∞ performance and optimal H2 performance index. Finally, a numerical example shows the design procedures and the effectiveness of the designed method. Key words： T-S fuzzy systems; Reliable quadratic stability; H2/H∞ mixed control; Linear matrix inequalities