时滞LPV重复过程的H_∞模型降阶  

H_∞ Model Reduction of Time-delayed LPV Repetitive Processes

作　　者：齐迹[1] 李艳辉[2] 梁艳[2] 

机构地区：[1]齐齐哈尔大学通信与电子工程学院,黑龙江齐齐哈尔161006 [2]东北石油大学电气信息工程学院,黑龙江大庆163318

出　　处：《科技通报》2016年第1期24-30,43,共8页Bulletin of Science and Technology

基　　金：国家杰出青年基金项目(61004067);黑龙江省自然科学基金项目(QC2011C043);齐齐哈尔大学青年教师项目(2012k-M08)

摘　　要：将时滞线性参数变化(LPV)思想应用于重复过程中,研究了其H∞模型降阶问题。目的是设计一个低阶的LPV重复过程来近似原高阶的LPV重复过程,使得误差在性能指标下达到最小。首先基于参数依赖Lyapunov函数方法推出了该误差过程的稳定性和降阶模型设计的充分条件。进一步通过投影定理引入两个附加矩阵,解除了重复过程矩阵和依赖于参数的Lyapunov函数矩阵之间的耦合,使得到的条件便于求解。仿真实例证实了该设计方法的有效性。The paper investigates the problem of H∞model reduction for a class of time-delayed linear parameter varying repetitive processes. Our pupose is focused on the construction of a reduced-order stable LPV repetitive processes, Such that the H ∞ gain of the error processes between the original processes and reduced-order one is less than a prescribed scalar. Sufficient conditions for the analysis of stability and the existence of the reduced-order are proposed, which are first established in terms of the parameter-dependent Lyapunov functions.Using the projection lemma and with the help of two slack matrices, the parameter-dependent Lyapunov functions matrices and the repetitive processes matrices are decoupled so that the problem is solved. A numerical example illustrates the effectiveness of the proposed design scheme.

关 键 词：线性参数变化重复过程 参数依赖LYAPUNOV函数 参数线性矩阵不等式 H∞模型降阶 

分 类 号：O231.1[理学—运筹学与控制论]