模型误差变化率有界的空间连接系统鲁棒性能分析  

Robust Performance Analysis of Spatially Interconnected Systems with Rate-of-variation Bounded Time-varying and Space-varying Uncertainties

作　　者：刘华波[1,2] 周彤[1,3] 

机构地区：[1]清华大学自动化系,北京100084 [2]青岛大学自动化工程学院,青岛266071 [3]清华信息科学与技术国家实验室,北京100084 [4]清华信息科学与技术国家实验室北京100084

出　　处：《自动化学报》2014年第10期2098-2107,共10页Acta Automatica Sinica

基　　金：国家重点基础研究发展计划(973计划)(2009CB320602);国家自然科学基金(61174122;61021063)资助~~

摘　　要：针对具有时空不变名义模型的空间连接系统,讨论其存在有界、线性、时空变化和有结构性约束的模型误差时,取得鲁棒性能的条件.对于时间轴和空间轴,分别定义了算子的时间变化率和空间变化率,给出了系统取得鲁棒性能时该变化率的上界和下界.研究表明,对于时间轴和空间轴上变化率满足一定条件、具有结构约束的有界模型误差,系统取得鲁棒性能的充分必要条件是存在频率域上的缩放矩阵(D标度),使得系统名义模型范数小于1.This paper investigates robust performance for a kind of spatially interconnected dynamic systems under bounded, linear, time-varying, space-varying, structured uncertainties. Both temporal rate-of-variation and spatial rate- of-variation are introduced to a linear time-varying and space-varying operator. On the premise of guaranteeing robust performances, both upper and lower bounds are obtained for the maximal rate-of-variation of uncertainties. It is proved that the existence of a temporal and spatial frequency dependent D-scale matrix that can render the norm of the nominal model less than one is necessary and sufficient for robust performances against time-varying and space-varying structured bounded uncertainties with appropriate rate-of-variations.

关 键 词：空间连接系统 鲁棒性能 模型误差 非因果性 结构不确定性 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程]