Absolute instability of Lur'e systems and its application to oscillation analysis of uncertain genetic networks
Absolute instability of Lur'e systems and its application to oscillation analysis of uncertain genetic networks
复制标题
Lure系统的绝对不稳定性及其在不确定遗传网络振荡分析中的应用
DOI：
10.1002/rnc.3294
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发表时间：
2014
影响因子：
3.9
通讯作者：
Kazuyuki Aihara
中科院分区：
文献类型：
--
作者：
Masaki Inoue;Jun-ichi Imura;Kenji Kashima;Masayasu Suzuki;Kazuyuki Aihara
我们推导了具有扇区有限非线性和不确定外部信号的 Lur'e 系统的不稳定性标准。首先，我们定义平衡的绝对不稳定，并根据线性矩阵不等式导出固定平衡点的绝对不稳定条件，这类似于众所周知的圆稳定性准则。然后，将该条件推广为参数绝对不稳定条件，适用于平衡点位置受不确定非线性和不确定外部信号影响的Lur'e系统的不稳定测试。最后，我们通过不确定遗传网络模型的振荡分析表明所提出的分析方法是有用的。版权所有 © 2014 约翰·威利父子有限公司
We derive instability criteria for Lur'e systems with sector‐bounded nonlinearities and uncertain external signals. First, we define absolute instability of an equilibrium and derive an absolute instability condition for a fixed equilibrium point in terms of a linear matrix inequality, which is analogous to the well‐known circle stability criterion. Then, the condition is extended to a parametric absolute instability condition, which is applicable to the instability test of a Lur'e system with an equilibrium point whose location is affected by uncertain nonlinearities and uncertain external signals. Finally, we show that the proposed analysis method is useful through the oscillation analysis of an uncertain genetic network model. Copyright © 2014 John Wiley & Sons, Ltd.