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