Improved stability conditions for time-varying delay systems via relaxed Lyapunov functionals

被引：8

作者：

Wang, Xin ^{[1
]}

Sun, Jian ^{[1
,2
]}

Wang, Gang ^{[1
,2
]}

Dou, Lihua ^{[1
,2
]}

机构：

[1] Beijing Inst Technol, State Key Lab Intelligent Control & Decis Comple, Beijing 100081, Peoples R China

[2] Beijing Inst Technol, Chongqing Innovat Ctr, Chongqing 401120, Peoples R China

来源：

INTERNATIONAL JOURNAL OF CONTROL | 2023年 / 96卷 / 06期

基金：

国家重点研发计划; 中国国家自然科学基金;

关键词：

Time-varying delay; stability; relaxed Lyapunov functionals; INEQUALITY APPLICATION; LINEAR-SYSTEMS; MATRIX;

D O I：

10.1080/00207179.2022.2056716

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

In this paper, the stability analysis of linear systems with time-varying delays is studied. A novel Lyapunov method is presented, in which positive definiteness of the matrices in common Lyapunov functionals is relaxed by adding what is referred to as a zero-integral functional (ZIF). A general form of auxiliary polynomial-based functionals that contains such ZIF is given. Choosing polynomials of different order as well as exploring double-delay-product (DDP) terms, novel Lyapunov functionals are constructed, which contribute to a set of improved stability conditions expressed in terms of linear matrix inequalities. Finally, numerical examples are provided to corroborate the merits of the proposed method relative to a number of existing methods, and in particular, the effectiveness of the proposed ZIFs and DDP terms in reducing the conservatism of stability conditions.

引用

页码：1568 / 1581

页数：14

共 47 条

[1]

[Anonymous], 2014, INTRO TIME DELAY SYS, DOI DOI 10.1007/978-3-319-09393-2

[2] From Unmanned Systems to Autonomous Intelligent Systems [J].

Chen, Jie ;

Sun, Jian ;

Wang, Gang .

ENGINEERING, 2022, 12 :16-19

[3] 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

[4] How often should one update control and estimation: review of networked triggering techniques [J].

Chen, Zhiyong ;

Han, Qing-Long ;

Yan, Yamin ;

Wu, Zheng-Guang .

SCIENCE CHINA-INFORMATION SCIENCES, 2020, 63 (05)

[5] Improved delay-dependent stability criteria for linear systems with multiple time-varying delays [J].

de Oliveira, Fulvia S. S. ;

Souza, Fernando O. .

INTERNATIONAL JOURNAL OF CONTROL, 2021, 94 (12) :3415-3423

[6] 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

[7]

Fan G, 2017, NERI INDEX MARKETIZA

[8]

Gu K., 2003, CONTROL ENGN SER BIR

[9] Augmented Lyapunov functional and delay-dependent stability criteria for neutral systems [J].

He, Y ;

Wang, QG ;

Lin, C ;

Wu, M .

INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, 2005, 15 (18) :923-933

[10] Manned Aircraft and Unmanned Aerial Vehicle Heterogeneous Formation Flight Control via Heterogeneous Pigeon Flock Consistency [J].

Huo, Mengzhen ;

Duan, Haibin ;

Ding, Xilun .

UNMANNED SYSTEMS, 2021, 9 (03) :227-236

← 1 2 3 4 5 →