东北大学学报（自然科学版）

东北大学学报(自然科学版) ›› 2013, Vol. 34 ›› Issue (6): 770-773.DOI: -

• 信息与控制 • 上一篇    下一篇

具有时变时滞的广义系统的稳定性判别方法

郑连伟，宋叔尼   

  1. (东北大学理学院，辽宁沈阳110819)
  • 收稿日期:2012-11-30 修回日期:2012-11-30 出版日期:2013-06-15 发布日期:2013-12-31
  • 通讯作者: 郑连伟
  • 作者简介:郑连伟(1963-)，男，辽宁新民人，东北大学副教授，博士；宋叔尼(1962-)，男，湖南澧县人，东北大学教授，博士.
  • 基金资助:
    辽宁省自然科学基金资助项目(201102070).

Stability Criteria for Descriptor Systems with TimeVarying Delay

ZHENG Lianwei， SONG Shuni   

  1. School of Sciences， Northeastern University， Shenyang 110819， China.
  • Received:2012-11-30 Revised:2012-11-30 Online:2013-06-15 Published:2013-12-31
  • Contact: ZHENG Lianwei
  • About author:-
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摘要： 针对时滞是时变的且属于一个区间的情况，研究时滞广义系统的稳定性问题.利用4个线性矩阵不等式给出了系统正则、无脉冲且渐近稳定的判别方法.把时滞区间分成两个相等的子区间，对应于每个子区间，利用适当的不等式对积分的系数进行放大，把Lyapunov-Krasovskii泛函导数的上界表示成某个参数的仿射函数.用两个线性矩阵不等式保证该导数的负定性，进而推广了文献中的凸组合方法.理论分析和数值算例表明，所得结果比现有结果具有更小的保守性.

关键词: 时变时滞, 广义系统, 稳定性, Lyapunov-Krasovskii泛函, 线性矩阵不等式

Abstract: Due to the delay is timevarying and ranges in an interval， the problem of stability for descriptor systems with a delay was investigated. A criterion guaranteeing regularity， free impulse and asymptotic stability were formulated in terms of four linear matrix inequalities. The delay interval was partitioned into two equal subintervals， for each of which， the coefficients of the integrals were enlarged by appropriate inequalities. The upper bound of the derivative of the LyapunovKrasovskii functional was expressed as an affine function with respect to some parameter. Two linear matrix inequalities were derived to guarantee the negativity of such derivative. Therefore， the convex combination method in the literature had been generalized. Theoretical analysis and an example showed the result obtained was less conservative than those of some existing ones.

Key words: timevarying delay, descriptor systems, stability, LyapunovKrasovskii functional, linear matrix inequalities

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