不确定多时滞非线性系统的H_∞模型简化问题研究  

On H-Infinite Model Reduction for Uncertain Nonlinear Systems with Multiple Time Delays

作　　者：贾秋玲[1] 吴成富[1] 王新民[1] 

机构地区：[1]西北工业大学自动化学院,陕西西安710072

出　　处：《西北工业大学学报》2004年第3期350-354,共5页Journal of Northwestern Polytechnical University

基　　金：国家重点基础研究发展规划项目 (G19980 30 4 17)资助

摘　　要：为得到 H∞ 模型简化问题的更具一般性的结论 ,利用线性矩阵不等式方法研究了一类不确定有界的多时滞非线性系统的 H∞ 模型简化问题。给出了该类问题有解的充分条件和简化模型的求解步骤。文中指出只要相应的矩阵不等式的正定解存在 ,就能够将研究的系统简化为低阶线性时滞系统、线性系统甚至零阶输入输出映射。算例仿真表明简化的模型能够较好地近似原复杂系统。To obtain general results concerning the H-infinite model reduction problems, a kind of uncertain nonlinear systems with multiple time delays and bounded uncertainty is studied. Our main contribution is a theorem that gives the sufficient conditions for the solvability of the H-infinite model reduction problems for a kind of uncertain nonlinear systems with multiple time delays. The methods to obtain the simplified model are also given. It is pointed out that this kind of nonlinear systems can be simplified into low-order linear systems with or without time delay, or even into a zero order mapping from input to output as long as the relevant linear matrix inequalities (LMI) are solvable. Simulation results illustrate that the simplified model can well approximate the original complicated nonlinear system.

关 键 词：不确定性 多时滞 H∞模型简化 线性矩阵不等式 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程]