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

作　　者：吴玉彬 张合新 惠俊军 李国梁 周鑫 杨田光 WU Yu-bin;ZHANG He-xin;HUI Jun-jun;LI Guo-liang;ZHOU Xin;YANG Tian-guang(Rocket Force University of Engineering,Xi’an,Shaanxi 710025,China;MailBox 150 Extension 11,Baoji,Shaanxi 721013,China;School of Astronautics,Northwestern Polytechnical University,Xi’an,Shaanxi 710072,China)

机构地区：[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

出　　处：《电子学报》2018年第4期975-983,共9页Acta Electronica Sinica

基　　金：国家自然科学基金(No.61374120)

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.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.

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 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程]