基于Wirtinger型积分不等式的线性时滞广义系统稳定性准则

doi:10.16183/j.cnki.jsjtu.2020.147

上海交通大学学报 ›› 2020, Vol. 54 ›› Issue (9): 967-972.doi: 10.16183/j.cnki.jsjtu.2020.147

• 制导、导航与控制专栏 • 上一篇下一篇

基于Wirtinger型积分不等式的线性时滞广义系统稳定性准则

朱金梁¹, 王婷¹(), 李涛²

1.南京林业大学信息科学技术学院, 南京 210037
2.南京航空航天大学自动化学院, 南京 211106

收稿日期:2020-05-25 出版日期:2020-09-28 发布日期:2020-10-10
通讯作者: 王婷 E-mail:chunchun1010@163.com
作者简介:朱金梁(1994-),男,江苏省盐城市人,硕士生,主要从事时滞控制系统分析和设计研究
基金资助:
国家自然科学基金项目(31700478);南京林业大学青年科技创新基金项目(CX2017032)

Stability Criteria of Linear Time-Delay Singular Systems Based on Wirtinger-Type Integral Inequality

ZHU Jinliang¹, WANG Ting¹(), LI Tao²

1. School of Information Science and Technology, Nanjing Forestry University,Nanjing 210037, China
2. School of Automation Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China

Received:2020-05-25 Online:2020-09-28 Published:2020-10-10
Contact: WANG Ting E-mail:chunchun1010@163.com

摘要/Abstract

摘要：

为研究线性时滞广义系统的渐近稳定性问题,利用时滞分割法均匀分割时滞区间,构造包含多重积分的Lyapunov-Krasovskii泛函以充分利用各子区间的时滞信息,并利用改进的Wirtinger型积分不等式估计泛函导函数的更紧上界,进而建立判定系统渐近稳定的时滞相关充分条件.最后,通过对比3个数值算例的仿真结果,证明了方法的有效性和先进性.

关键词: 时滞广义系统, 渐近稳定, Wirtinger型积分不等式, 线性矩阵不等式

Abstract:

Aimed at the asymptotic stability of linear time-delay singular system,the time-delay interval was evenly divided by using the time-delay division method, and a Lyapunov-Krasovskii functional (LKF) with multiple integral terms was constructed to effectively utilize the time-delay information of each sub-interval. Next, some improved Wirtinger-type integral inequalities were employed to estimate the LKF derivative and obtain a tighter estimation. Then, delay-dependent sufficient conditions were established to ensure the asymptotic stability of the addressed system. Finally, by using three numerical examples, comparisons and simulations were presented to illustrate the efficiency and superiority of the proposed method.

Key words: time-delay singular system, asymptotic stability, Wirtinger-type integral inequality, linear matrix inequality (LMI)

中图分类号:

TP13

朱金梁, 王婷, 李涛. 基于Wirtinger型积分不等式的线性时滞广义系统稳定性准则[J]. 上海交通大学学报, 2020, 54(9): 967-972.

ZHU Jinliang, WANG Ting, LI Tao. Stability Criteria of Linear Time-Delay Singular Systems Based on Wirtinger-Type Integral Inequality[J]. Journal of Shanghai Jiaotong University, 2020, 54(9): 967-972.

图/表 4

参考文献 20

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c	τ_max
c	文献[15]	文献[16](N=2)	文献[17]	定理1
1.2	3.1763	3.3657	3.8045	9.2198
1.4	2.5740	2.7167	3.0433	7.6275
1.6	2.1675	2.2814	2.5396	6.5287
2.0	1.6509	0.7310	1.9114	5.0937

方法	τ_max
文献[19]	1.5405
文献[4]	1.7122
文献[20]	1.7145
推论1	2.8985

基于Wirtinger型积分不等式的线性时滞广义系统稳定性准则

Stability Criteria of Linear Time-Delay Singular Systems Based on Wirtinger-Type Integral Inequality

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