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 孙大为 WU Yubin;ZHANG Hexin;HUI Junjun;LI Guoliang;ZHOU Xin;SUN Dawei(Department of Control and Engineering, Rocket Force University of Engineering, Xi’an 710025, China;Unit 96037 of the PLA, Baoji 721013, China;Department of Basic, Sergeancy School of Rocket Force, Qingzhou 262500, China)

机构地区：[1]火箭军工程大学控制工程系,陕西西安710025 [2]中国人民解放军96037部队,陕西宝鸡721013 [3]火箭军士官学校基础系,山东青州262500

出　　处：《系统工程与电子技术》2018年第4期878-884,共7页Systems Engineering and Electronics

基　　金：国家自然科学基金(61374120)资助课题

摘　　要：研究了一类线性区间变时滞不确定系统鲁棒稳定性问题。基于新型的时滞分割法和交互式凸组合技术,借助于构造包含四重积分项的新Lyapunov-Krasovskii泛函,并利用新的积分不等式界定方法给出了线性矩阵不等式形式的时滞相关稳定性判据。与已有文献相比,该判据扩大了保证系统稳定的最大时滞上界范围,在降低结论的保守性和提高计算效率两者间达到了一个很好的平衡。最后通过3个具有代表性的数值例子对比验证了该方法在降低结论保守性方面的优越性。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 terms is introduced.A novel delay dependent stability criterion in terms of linear matrix inequalities is given by using a new delay-partitioning approach and reciprocally convex combination technique,which is derived by a new integral inequality method.Compared with the existing literature,this criterion can extend the maximum allowable delay bound for the stability of the system,and achieve a good balance between the conservatism of conclusions and computational efficiency.Finally,three well-known numerical comparative examples are given to demonstrate the superiority of the proposed approach in reducing the conservation of conclusion.

关 键 词：区间变时滞 时滞分割 鲁棒稳定 交互式凸组合 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]