Comparison of bounding methods for stability analysis of systems with time-varying delays
Comparison of bounding methods for stability analysis of systems with time-varying delays
复制标题
时变时滞系统稳定性分析的边界方法比较
DOI：
10.1016/j.jfranklin.2017.02.007
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发表时间：
2017-05
期刊：
影响因子：
--
通讯作者：
re Seuret
中科院分区：
文献类型：
--
作者：
Kun Liu;Alex;re Seuret
二次函数的积分不等式在线性时滞系统时滞相关稳定性判据的推导中起着重要的作用。基于詹森不等式，Park等人提出了一种新的凸组合方法.（2011）推导了时滞相关的稳定性判据，得到了与Moon等人的上界相同的时变时滞上界。不平等最近，Seuret和Gouaisbaut（2013）提出了一个新的不等式，称为基于Wirtinger的不等式，它包含了詹森不等式，用于时滞系统的稳定性分析。本文证明了只有利用詹森不等式，双凸组合方法才是有效的。当詹森不等式被Wirtinger不等式所取代时，Moon集不等式结合凸分析可以得到比双凸组合不等式保守性更小的稳定性条件，并且证明了由Moon集不等式和凸分析导出的LMI条件的可行性蕴含了由双凸组合不等式导出的LMI条件的可行性.最后，数值算例表明，即使相应的零时滞系统和不含时滞项的系统都是不稳定的，该方法也是有效的。
Integral inequalities for quadratic functions play an important role in the derivation of delay-dependent stability criteria for linear time-delay systems. Based on the Jensen inequality, a reciprocally convex combination approach was introduced by Park et al. (2011) for deriving delay-dependent stability criterion, which achieves the same upper bound of the time-varying delay as the one on the use of the Moon’s et al. inequality. Recently, a new inequality called Wirtinger-based inequality that encompasses the Jensen inequality was proposed by Seuret and Gouaisbaut (2013) for the stability analysis of time-delay systems. In this paper,it is revealed that the reciprocally convex combination approach is effective only with the use of Jensen inequality. When the Jensen inequality is replaced by Wirtinger-based inequality, the Moon’set al.inequality together with convex analysis can lead to less conservative stability conditions than the reciprocally convex combination inequality.Moreover, we prove thatthe feasibility of an LMI condition derived by the Moon’set al.inequality as well as convex analysis implies the feasibility of an LMI condition induced by the reciprocally convex combination inequality.Finally, the efficiency of the methods is demonstrated by some numerical examples, even though the corresponding system with zero-delay as well as the system without the delayed term are not stable.
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影响因子：
3.9
作者：
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作者：
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影响因子：
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作者：
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影响因子：
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作者：
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DOI：
10.1016/j.automatica.2007.02.022
发表时间：
2007-10
期刊：
Autom.
影响因子：
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作者：
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通讯作者：
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