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山东大学学报(工学版) ›› 2015, Vol. 45 ›› Issue (1): 54-63.doi: 10.6040/j.issn.1672-3961.0.2014.140

• 控制科学与工程 • 上一篇    下一篇

不确定随机多时滞系统鲁棒随机稳定性分析

张慧慧, 夏建伟   

  1. 聊城大学数学科学学院, 山东 聊城 252000
  • 收稿日期:2014-05-16 修回日期:2014-11-28 发布日期:2014-05-16
  • 通讯作者: 夏建伟(1978-),男,山东潍坊人,副教授,博士,主要研究方向为随机系统鲁棒控制.E-mail:jianweixia78@gmail.com E-mail:jianweixia78@gmail.com
  • 作者简介:张慧慧(1991-),女,山东临沂人,硕士研究生,主要研究方向为多时滞系统稳定性.E-mail:zhhly0217@163.com
  • 基金资助:
    国家自然科学基金资助项目(61004046, 61104117)

Robust stochastic stability for uncertain stochastic system with multiple delays

ZHANG Huihui, XIA Jianwei   

  1. School of Mathematics Science, Liaocheng University, Liaocheng 252000, Shandong, China
  • Received:2014-05-16 Revised:2014-11-28 Published:2014-05-16

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摘要： 研究了一类不确定随机多时滞系统的鲁棒随机稳定性问题,其中系统不确定参数满足线性分式结构。首先,将倒数凸方法加以推广,得到一个新的积分不等式引理;然后,充分考虑时滞区间上下限关系,构造了多时滞区间相关的李雅普诺夫函数,并在新的积分不等式方法下,得到具有更小保守性和较少自由变量的时滞相关稳定性条件; 最后,给出一些数值仿真实例,验证了所提方法的有效性。

关键词: 线性结构不确定性, 多时滞, 李雅普诺夫函数, 随机系统, 鲁棒随机稳定, LMI

Abstract: The problem of robust stochastic stability for a class of uncertain stochastic systems with multiple delays was investigated in this paper. The uncertainties were in linear fractional form. Firstly, a new integral inequlity lemma was derived by extending the reciprocally convex approach. Then, based on a multiple delay-interval dependent Lyapunov-Krasovskii constructed by fully considering the relationship between upper and lower time delay interval and the new integral inequlity approach, some novel delay-dependent stability criteria with less conservatism and less free weighting matrices were obtained. At last, some numerical examples were given to show the effectiveness of the proposed results.

Key words: linear fractional uncertainties, multiple delays, stochastic system, robust stochastical stability, Lyapunov-Krasovskii function, LMI

中图分类号: 

  • O231.3
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