区间变时滞不确定系统鲁棒稳定性分析

doi:10.3969/j.issn.0372-2112.2018.04.028

电子学报 ›› 2018, Vol. 46 ›› Issue (4): 975-983.DOI: 10.3969/j.issn.0372-2112.2018.04.028

区间变时滞不确定系统鲁棒稳定性分析

吴玉彬¹, 张合新¹, 惠俊军², 李国梁¹, 周鑫¹, 杨田光³

1. 火箭军工程大学, 陕西西安 710025;
2. 宝鸡市150信箱11分箱, 陕西宝鸡 721013;
3. 西北工业大学航天学院, 陕西西安 710072

收稿日期:2016-12-14 修回日期:2017-04-07 出版日期:2018-04-25 发布日期:2018-04-25
作者简介:吴玉彬 男,1984年2月出生,山西稷山人.分别于2007年和2011年在第二炮兵工程大学获得工学学士和工学硕士学位,现为火箭军工程大学控制工程系博士.研究方向为时滞系统鲁棒稳定性与鲁棒镇定.E-mail:59153220@qq.com;张合新 男,1965年7月出生,河北易县人.教授、博士生导师.1987年、1994年和2001年分别在第二炮兵工程学院、西北工业大学和第二炮兵工程学院获得工学学士、工学硕士和工学博士学位.现为火箭军工程大学控制工程系教授.主要从事飞行器制导与控制等方面的研究工作
基金资助:
国家自然科学基金（No.61374120）

Novel Robust Stability Condition for Uncertain Systems with Interval Time-Varying Delay

WU Yu-bin¹, ZHANG He-xin¹, HUI Jun-jun², LI Guo-liang¹, ZHOU Xin¹, YANG Tian-guang³

1. Rocket Force University of Engineering, Xi'an, Shaanxi 710025, China;
2. MailBox 150 Extension 11, Baoji, Shaanxi 721013, China;
3. School of Astronautics, Northwestern Polytechnical University, Xi'an, Shaanxi 710072, China

Received:2016-12-14 Revised:2017-04-07 Online:2018-04-25 Published:2018-04-25

摘要/Abstract

摘要： 本文针对一类线性区间变时滞不确定系统的鲁棒稳定性分析问题进行了研究.基于时滞中点法和凸组合技术，借助于构造一个包含四重积分项的新Lyapunov-Krasovskii（L-K）泛函，并利用积分不等式方法给出了LMI（Linear Matrix Inequality）形式的时滞相关稳定性新判据.与已有文献相比，该判据能大大降低理论推导和计算上的复杂性.最后通过三个具有代表性的数值例子对比验证了本文所提出方法在降低结论保守性方面的优越性.

关键词: 区间变时滞, Lyapunov-Krasovskii(L-K)泛函, 鲁棒稳定, 凸组合技术, 四重积分

Abstract: In this paper,the problem of robust stability analysis for a class of linear uncertain systems with interval time-varying delay is studied.In order to develop a less conservative stability condition,a Lyapunov-Krasovskii functional comprising quadruple-integral term is introduced.A novel delay dependent stability criterion in terms of linear matrix inequalities (LMIs) is given by using delay-central-point (DCP) method and reciprocally convex combination technique,which is derived by integral inequality method.Compared with the existing literature,this criterion can greatly reduce the complexity of theoretical derivation and computation.Finally,three well-known numerical comparative examples are given to verify the superiority of the proposed approach in reducing the conservation of conclusion.

Key words: interval time-varying delay, Lyapunov-Krasovskii functional, robust stability, reciprocally convex combination, quadruple-integral term

中图分类号:

TP13

吴玉彬, 张合新, 惠俊军, 李国梁, 周鑫, 杨田光. 区间变时滞不确定系统鲁棒稳定性分析[J]. 电子学报, 2018, 46(4): 975-983.

WU Yu-bin, ZHANG He-xin, HUI Jun-jun, LI Guo-liang, ZHOU Xin, YANG Tian-guang. Novel Robust Stability Condition for Uncertain Systems with Interval Time-Varying Delay[J]. Acta Electronica Sinica, 2018, 46(4): 975-983.

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区间变时滞不确定系统鲁棒稳定性分析

Novel Robust Stability Condition for Uncertain Systems with Interval Time-Varying Delay

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[1]	王占山;张化光;余文;张庆灵. 基于LMI的时变时滞Cohen-Grossberg神经网络鲁棒稳定性[J]. 电子学报, 2008, 36(11): 2220-2223.
[2]	季策;张化光;关焕新. 多时滞Cohen-Grossberg神经网络鲁棒稳定性的新判据[J]. 电子学报, 2007, 35(1): 135-140.
[3]	季策;张化光. 具有参数摄动的时滞Hopfield神经网络的鲁棒稳定性[J]. 电子学报, 2005, 33(1): 115-118.
[4]	季策;张化光. 具有参数摄动的时滞Hopfield神经网络的鲁棒稳定性[J]. 电子学报, 2005, 33(1): 115-118.