基于LMI的不确定非线性系统H<sub>∞</sub>控制

基于LMI的不确定非线性系统H_∞控制

摘要: 基于非线性系统的Takagi-Sugeno（T-S）模糊模型，研究了一类结构不确定非线性系统H_∞控制问题．利用线性矩阵不等式（LMI）方法，得到了模糊H_∞输出反馈控制器的系统化设计方法．考虑到子系统之间的相互作用，给出了H_∞输出反馈控制器存在的充分条件．这个充分条件只用一个矩阵不等式表示，形式简洁，放宽了控制器存在的充分条件．最后，以洛伦兹混沌系统为例，说明了该方法的有效性．

Abstract: Based on Takagi-Sugeno(T-S) fuzzy model of nonlinear systems,H_∞ control is studied for a class of nonlinear systems with structure uncertainties.The systematic design procedure of fuzzy H_∞ output feedback controllers is achieved via linear matrix inequality(LMI) approach.Interactions among the subsystems are considered and sufficient condition for existence of the fuzzy H_∞ output feedback controller is obtained.And the sufficient condition is expressed with only a matrix inequality,which is simple in form and relaxes the sufficient condition for the existence of the controller.Finally,Lorentz chaotic system is taken as an example to demonstrate the validity of the proposed controller.