基于自由矩阵型不等式的分布时滞系统稳定性分析  

Stability Analysis for Systems with Distributed Delay via Free-Matrix-Based Integral Inequality

作　　者：刘臻臻[1] 林崇[1] 赵南[1] 龚冠桦 

机构地区：[1]青岛大学复杂性科学研究所,山东青岛266071

出　　处：《青岛大学学报（工程技术版）》2016年第4期1-5,共5页Journal of Qingdao University(Engineering & Technology Edition)

基　　金：国家自然科学基金资助项目(61174033);山东省自然科学基金资助项目(ZR2011FM006)

摘　　要：针对分布时滞系统的稳定性问题,本文基于应用自由权矩阵技术,推导出一个改进型的二重积分不等式,完成对分布时滞系统的稳定性分析。通过构造适当的Lyapunov-Krasovskii泛函,并应用二重积分不等式,得到更好的判断系统稳定性的充分条件,最后利用数例进行计算验证。验证结果表明,利用本文分析方法得到结果的最大时滞上界值均大于文献[2]的值,且更接近于理论值。应用不等式进行分析得到的结果与应用Wirtinger型双重积分不等式得到的结果相比,具有更低的保守性。该研究对于提高系统的稳定性分析方法具有重要意义。In this paper, an improved double integral inequality is derived by using free-weighting-matrix tech-nique. In order to analyze the stability of linear systems with discrete distributed delays, an appropriateL- Kfunctional is constructed and this newly proposeddouble integral inequality is employed. Better sufficient con-ditions are thus obtained in items of LMIs for the stability test. Finally, we can demonstrate its effectiveness by using numerical examples. The calculations show that the upper bound of the maximum time-delay obtained by using our analysis method is bigger than those in[2]. This verifies that the results applying this new inequality are of less conservatism compared with those applying the double wirtinger-based integral inequality. Our theo-retical research has certain significance to improve the methods of stability analysis for time-delay systems.

关 键 词：分布时滞系统 Lyapunov-Krasovskii泛函法 自由矩阵型不等式 

分 类 号：O175[理学—数学]