Refined Jensen-Based Multiple Integral Inequality and Its Application to Stability of Time-Delay Systems

被引：6
作者：
Wang, Jidong [1 ,2 ,3 ]
Wang, Zhanshan [1 ,2 ]
Ding, Sanbo [1 ,2 ]
Zhang, Huaguang [1 ,2 ]
机构：
[1] Northeastern Univ, Coll Informat Sci & Engn, Shenyang 110819, Liaoning, Peoples R China
[2] State Key Lab Synthet Automat Proc Ind, Shenyang 110819, Liaoning, Peoples R China
[3] North China Univ Water Resources & Elect Power, Coll Elect Engn, Zhengzhou 450011, Henan, Peoples R China
来源：
IEEE-CAA JOURNAL OF AUTOMATICA SINICA | 2018年 / 5卷 / 03期
基金：
中国国家自然科学基金;
关键词：
Multiple integral approach; refined Jensen-based multiple integral inequality (RJMII); stability analysis; time-delay systems; BARRIER LYAPUNOV FUNCTIONS; ADAPTIVE-CONTROL; FUNCTIONALS;
D O I：
10.1109/JAS.2018.7511087
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
This paper investigates the stability of time-delay systems via a multiple integral approach. Based on the refined Jensen-based inequality, a novel multiple integral inequality is proposed. Applying the multiple integral inequality to estimate the derivative of Lyapunov-Krasovskii functional (LKF) with multiple integral terms, a novel stability condition is formulated for the linear time-delay systems. Two numerical examples are employed to demonstrate the improvements of our results.
引用
收藏
页码：758 / 764
页数：7
相关论文
共 34 条
[1]  
[Anonymous], 2001, LECT NOTES CONTROL I
[2]   Single/Multiple Integral Inequalities With Applications to Stability Analysis of Time-Delay Systems [J].
Chen, Jun ;
Xu, Shengyuan ;
Zhang, Baoyong .
IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2017, 62 (07) :3488-3493
[3]   Wirtinger-basedmultiple integral inequality for stability of time-delay systems [J].
Ding, Sanbo ;
Wang, Zhanshan ;
Zhang, Huaguang .
INTERNATIONAL JOURNAL OF CONTROL, 2018, 91 (01) :12-18
[4]   A multiple integral approach to stability of neutral time-delay systems [J].
Fang, Mei ;
Park, Ju H. .
APPLIED MATHEMATICS AND COMPUTATION, 2013, 224 :714-718
[5]   Tutorial on Lyapunov-based methods for time-delay systems [J].
Fridman, Emilia .
EUROPEAN JOURNAL OF CONTROL, 2014, 20 (06) :271-283
[6]  
GU K., 2003, CONTROL ENGN SER BIR
[7]   A discrete delay decomposition approach to stability of linear retarded and neutral systems [J].
Han, Qing-Long .
AUTOMATICA, 2009, 45 (02) :517-524
[8]  
Jiang Yinlu, 2017, [自动化学报, Acta Automatica Sinica], V43, P1465
[9]   On the Liapunov-Krasovskii functionals for stability analysis of linear delay systems [J].
Kolmanovskii, VB ;
Niculescu, SI ;
Richard, JP .
INTERNATIONAL JOURNAL OF CONTROL, 1999, 72 (04) :374-384
[10]  
Last E., 1994, Proc. IEEE, V86, P2473
1234