Journal of Jilin University(Engineering and Technology Edition) ›› 2018, Vol. 48 ›› Issue (5): 1556-1562.doi: 10.13229/j.cnki.jdxbgxb20180320

Previous Articles     Next Articles

Stability analysis of linear systems with interval time-varying delay

YAN Dong-mei1, ZHONG Hui1, REN Li-li2, WANG Ruo-lin3, LI Hong-mei1   

  1. 1.Management Center of Big Data and Network, Jilin University, Changchun 130012,China;
    2.Network Center, Changchun Normal University, Changchun 130032,China;
    3.College of Administrative Engineering,Jilin Communications Polytechnic, Changchun 130012,China
  • Received:2017-11-22 Online:2018-09-20 Published:2018-12-11

RICH HTML

 0   

PDF (PC)

69

Abstract: This paper investigates the stability problem of a linear system with time-varying delay. The time-varying delay is assumed to belong to a given interval. A new Lyapunov-Krasovskii function is constructed which contains some tripe integral terms. Using some integral inequalities including the recent proposed free-matrix-based integral inequality, new sufficient stability conditions are obtained, which are presented in terms of Linear Matrix Inequality (LMI). Finally, two examples are given to demonstrate that the obtained results are less conservative than some existing method.

Key words: automatic control technology, time-delay system, delay-dependent stability, interval delay, linear matrix inequality

CLC Number: 

  • TP273
[1] Sun J, Liu G P, Chen J, et al.Networked predictive control for Hammerstein systems[J]. Asian Journal of Control, 2011, 13: 265-272.
[2] Sun J, Chen J.Networked predictive control for systems with unknown or partially known delay[J]. IET Control Theory Appl,2014,8(18):2282-2288.
[3] 李学军,陈虹,于树友.基于时滞系统的无偏H∞滤波[J].吉林大学学报:工学版,2009,39(2):473-479.
Li Xue-jun, Chen Hong, Yu Shu-you.Unbiased H∞filtering for time delay system[J].Journal of Jilin University(Engineering and Technology Edition),2009,39(2):473-479.
[4] Fridman E, Shaked U.Delay-dependent stability and H∞ control: constant and time-varying delays[J].International Journal of Control, 2003, 76: 48-60.
[5] Fridman E, Shaked U.An improved stabilization method for linear systems with time-delay[J]. IEEE Transactions on Automatic Control, 2002, 47: 1931-1937.
[6] He Y, Wang Q G, Lin C, et al.Augmented Lyapunov functional and delay-dependent stability criteria for neutral systems[J].International Journal of Robust and Nonlinear Control, 2005,15:923-933.
[7] He Y, Wang Q G, Xie L, et al.Delay-range-dependent stability for systems with time-varying delay[J]. Automatica, 2007, 43: 371-376.
[8] He Y, Wang Q G, Xie L, et al.Further improvement of free-weighting matrices technique for systems with time-varying delay[J]. IEEE Transactions on Automatic Control, 2007,52:293-299.
[9] He Y, Wu M, She J H, et al.Delay-dependent robust stability criteria for uncertain neutral systems with mixed delays[J]. Systems & Control Letters, 2004, 51: 57-65.
[10] He Y, Wu M, She J H, et al.New delay-dependent stability criteria for robust stability of time-varying delay systems[J].Automatica, 2004, 40: 1435-1439.
[11] Sun J, Liu G P, Chen J, et al.Improved delay-range-dependent stability criteria for linear systems with time-varying delays[J].Automatica, 2010, 46: 466-470.
[12] Sun J, Han Q L, Chen J, et al.Less conservative stability criteria for linear systems with interval time-varying delays[J].International Journal of Robust and Nonlinear Control, 2015, 25: 475-485.
[13] Gu K.Integral inequality in the stability problem of time-delay systems[C]∥Proceedings of the 39th IEEE Conference on Decision and Control, Sydney, Australia, 2000,3:2805-2810.
[14] Seuret A, Gouaisbaut F.Wirtinger-based integral inequality: application to time-delay systems[J].Automatica, 2013, 49: 2860-2866.
[15] Park P, Ko J W.Stability and robust stability for systems with a time-varying delay[J].Automatica, 2007, 43: 1855-1858.
[16] Park P, Ko J W, Jeong C.Reciprocally convex approach to stability of systems with time-varying delays[J]. Automatica, 2011, 47: 235-238.
[17] Gu K, Han Q L, Luo A C J, et al. Discretized lyapunov functional for systems with distributed delay and piecewise constant coefficients[J].International Journal of Control, 2001, 74: 737-744.
[18] Gouaisbaut F, Peaucelle D.Delay-dependent robust stability of time delay systems[C]∥Proceedings of IFAC Symposium on Robust Control Design, Toulouse, France, 2006,5:453-458.
[19] Han Q L.New stability criteria for linear systems with interval time-varying delay[J]. Automatica, 2008, 44: 2680-2685.
[20] Hui Jun-jun, Zhang He-xin, Kong Xiang-yu, et al.On improved delay-dependent robust stability criteria for uncertain systems with interval time-varying delay[J].International Journal of Automation and Computing,2015,12(1):102-108.
[21] Fridman E.Tutorial on Lyapunov-based methods for time-delay systems[J]. European Journal of Control,2014,20(6):271-283.
[22] Zeng H B, He Y, Wu M, et al.Free-matrix-based integral inequality for stability analysis of systems with time-varying delay[J]. IEEE Transactions on Automatic Control, 2015, 60(10): 2768-2772.
[23] Sun J, Chen J.A survey on Lyapunov-based methods for stability of linear time-delay systems[J]. Frontiers of Computer Science,2017,11(4):555-567.
[24] Liu K, Fridman E, Johansson K H, et al.Generalized Jensen inequalities with application to stability analysis of systems with distributed delays over infinite time-horizons[J]. Automatica, 2016, 69: 222-231.
[25] Kim J H.Further improvement of Jensen inequality and application to stability of time-delayed systems[J]. Automatica, 2016,64:121-125.
[1] GU Wan-li,WANG Ping,HU Yun-feng,CAI Shuo,CHEN Hong. Nonlinear controller design of wheeled mobile robot with H∞ performance [J]. Journal of Jilin University(Engineering and Technology Edition), 2018, 48(6): 1811-1819.
[2] LI Zhan-dong,TAO Jian-guo,LUO Yang,SUN Hao,DING Liang,DENG Zong-quan. Design of thrust attachment underwater robot system in nuclear power station pool [J]. Journal of Jilin University(Engineering and Technology Edition), 2018, 48(6): 1820-1826.
[3] WANG De-jun, WEI Wei-li, BAO Ya-xin. Actuator fault diagnosis of ESC system considering crosswind interference [J]. Journal of Jilin University(Engineering and Technology Edition), 2018, 48(5): 1548-1555.
[4] TIAN Yan-tao, ZHANG Yu, WANG Xiao-yu, CHEN Hua. Estimation of side-slip angle of electric vehicle based on square-root unscented Kalman filter algorithm [J]. 吉林大学学报(工学版), 2018, 48(3): 845-852.
[5] ZHANG Shi-tao, ZHANG Bao, LI Xian-tao, WANG Zheng-xi, TIAN Da-peng. Enhancing performance of FSM based on zero phase error tracking control [J]. 吉林大学学报(工学版), 2018, 48(3): 853-858.
[6] WANG Lin, WANG Hong-guang, SONG Yi-feng, PAN Xin-an, ZHANG Hong-zhi. Behavior planning of a suspension insulator cleaning robot for power transmission lines [J]. 吉林大学学报(工学版), 2018, 48(2): 518-525.
[7] HU Yun-feng, WANG Chang-yong, YU Shu-you, SUN Peng-yuan, CHEN Hong. Structure parameters optimization of common rail system for gasoline direct injection engine [J]. 吉林大学学报(工学版), 2018, 48(1): 236-244.
[8] ZHU Feng, ZHANG Bao, LI Xian-tao, WANG Zheng-xi, ZHANG Shi-tao. Gyro signal processing based on strong tracking Kalman filter [J]. 吉林大学学报(工学版), 2017, 47(6): 1868-1875.
[9] JIN Chao-qiong, ZHANG Bao, LI Xian-tao, SHEN Shuai, ZHU Feng. Friction compensation strategy of photoelectric stabilized platform based on disturbance observer [J]. 吉林大学学报(工学版), 2017, 47(6): 1876-1885.
[10] FENG Jian-xin. Recursive robust filtering for uncertain systems with delayed measurements [J]. 吉林大学学报(工学版), 2017, 47(5): 1561-1567.
[11] XU Jin-kai, WANG Yu-tian, ZHANG Shi-zhong. Dynamic characteristics of a heavy duty parallel mechanism with actuation redundancy [J]. 吉林大学学报(工学版), 2017, 47(4): 1138-1143.
[12] HU Yun-feng, GU Wan-li, LIANG Yu, DU Le, YU Shu-you, CHEN Hong. Start-stop control of hybrid vehicle based on nonlinear method [J]. 吉林大学学报(工学版), 2017, 47(4): 1207-1216.
[13] SHEN Shuai, ZHANG Bao, LI Xian-tao, ZHU Feng, JIN Chao-qiong. Acceleration feedback control based on tracking differentiator [J]. 吉林大学学报(工学版), 2017, 47(4): 1217-1224.
[14] SHAO Ke-yong, CHEN Feng, WANG Ting-ting, WANG Ji-chi, ZHOU Li-peng. Full state based adaptive control of fractional order chaotic system without equilibrium point [J]. 吉林大学学报(工学版), 2017, 47(4): 1225-1230.
[15] WANG Chun-yang, XIN Rui-hao, SHI Hong-wei. Decreasing time delay auto-disturbance rejection control method for large time delay systems [J]. 吉林大学学报(工学版), 2017, 47(4): 1231-1237.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
[1] ZHU Jian-feng, LIN Yi, CHEN Xiao-kai, SHI Guo-biao. Structural topology optimization based design of automotive transmission housing structure[J]. 吉林大学学报(工学版), 2013, 43(03): 584 -589 .
[2] ZHOU Feng-dao, WANG Jin-yu, TANG Hong-zhong, ZHANG He, ZHOU Ji-yu. Multi-frequency digital drive signal generation technology in near surface electromagnetic detection domain[J]. 吉林大学学报(工学版), 2013, 43(03): 682 -687 .
[3] OUYANG Ji-hong, WANG Zhen-xin, JING Li. Expanding 9-intersection model with metric relations[J]. 吉林大学学报(工学版), 2013, 43(03): 695 -700 .
[4] GUO Tie-liang, ZHAO Dan-feng, YANG Da-wei. Efficient Doppler estimation for UWA OFDM systems[J]. 吉林大学学报(工学版), 2013, 43(03): 813 -818 .
[5] HE Yao, LIU Xing-tao, ZHANG Chen-bin, CHEN Zong-hai. Insulation detection algorithm for high-power battery system based on internal resistance model[J]. 吉林大学学报(工学版), 2013, 43(05): 1165 -1170 .
[6] LI Zhi-bin, JIN Mao-jing, LIU Pan, XU Cheng-cheng. Evaluation of impact variable speed limits on improving traffic efficiency on freeways[J]. 吉林大学学报(工学版), 2013, 43(05): 1204 -1209 .
[7] YUAN Zhe, MA Wen-xing, LIU Chun-bao, LIU Hao. Temperature field analysis of the open-type hydrodynamic retarder of heavy vehicle[J]. 吉林大学学报(工学版), 2013, 43(05): 1271 -1275 .
[8] SUI Zhou, CAI Zhong-yi, LAN Ying-wu, LI Ming-zhe. Shape control model for three-dimensional surface part in continuous flexible forming process[J]. 吉林大学学报(工学版), 2013, 43(05): 1302 -1306 .
[9] YANG Xiao-jun, SONG Qing-song, MA Xiang, LI Dong-hai. Fault-tolerance target tracking based on multi-model information filtering[J]. 吉林大学学报(工学版), 2013, 43(05): 1381 -1385 .
[10] WU Wen, MENG Xiang-ru, LIU Yun-jiang, HUO Xing-lin. Modeling and quantification of network survivability based on continuous time Markov[J]. 吉林大学学报(工学版), 2013, 43(05): 1395 -1400 .
Copyright © Journal of Jilin University(Engineering and Technology Edition), All Rights Reserved.
Tel: +86-431-85095297　Fax: +86-431-85094074　E-mail: xbgxb@jlu.edu.cn
Powered by Beijing Magtech Co. Ltd