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改进的区间变时滞基因调控网络稳定性准则

吴海霞1,2,冯 伟2,冉 维2   

  1. (1. 重庆大学自动化学院,重庆 400044;2. 重庆第二师范学院数学与信息工程系,重庆 400065)
  • 收稿日期:2013-05-27 出版日期:2014-06-15 发布日期:2014-06-13
  • 作者简介:吴海霞(1979-),女,副教授、博士后、CCF会员,主研方向:神经网络,基因调控网络动力学行为研究;冯 伟,副教授、博士、CCF会员;冉 维,讲师、硕士。
  • 基金项目:
    国家自然科学基金资助项目(61170249, 61103211);重庆市青年骨干教师计划基金资助项目(2011)。

Improved Stability Criteria for Genetic Regulatory Network with Interval Time-varying Delay

WU Hai-xia  1,2, FENG Wei  2, RAN Wei   2   

  1. (1. College of Automation, Chongqing University, Chongqing 400044, China;2. Department of Mathematics and Information Engineering, Chongqing University of Education, Chongqing 400065, China)
  • Received:2013-05-27 Online:2014-06-15 Published:2014-06-13

摘要: 为提高带区间变时滞基因调控网络的全局稳定性,利用李亚普诺夫泛函、线性矩阵不等式方法和新的积分不等式,得到一类改进基因调控网络的全局渐近稳定性判定条件。该稳定性准则不仅考虑时滞的时变因素,而且考虑时滞的上界和下界,由于采用新的积分不等式,使得这些结果具有更小的保守性且参数较少,对人工设计基因芯片可提供一定的参考。通过2个数值实例证明了理论结果的有效性。

关键词: 全局渐近稳定性, 基因调控网络, 区间变时滞, 线性矩阵不等式, 李亚普诺夫泛函, 平衡点

Abstract: In view of the global asymptotical stability of the genetic regulatory network with interval time-varying delays, this paper employs the Lyapunov-Krasovskii functional with Linear Matrix Inequality(LMI) techniques and new integral inequality approach, and derives some improved stability criteria. The present result takes into account the relationship between the time-varying delays and their lower and upper bounds. Due to the new integral inequality approach, the proposed method contains the least number of computed variables while maintaining the effectiveness of the stability conditions. The result can provide some reference for the design of gene chip. Two numerical examples are given to demonstrate the effectiveness and the benefits of the proposed method.

Key words: global asymptotical stability, genetic regulatory network, interval time-varying delay, Linear Matrix Inequality(LMI), Lyapunov functional, equilibrium point

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