Approach to delay-dependent robust stability and stabilisation of delta operator systems with time-varying delays

被引：11
作者：
El Aiss, Hicham [1 ]
Rachid, Hafsaa [1 ]
Hmamed, Abdelaziz [1 ]
El Hajjaji, Ahmed [2 ]
机构：
[1] Univ Sidi Mohammed Ben Abdellah, Fac Sci Dhar El Mehraz, Dept Phys, BP 1796, Fes, Fes, Morocco
[2] Univ Picardie Jules Vene, Modeling Informat & Syst Lab UFR Sci, MIS Lab UFR Sci, 33 Rue ST Leu, F-80000 Amiens, France
来源：
IET CONTROL THEORY AND APPLICATIONS | 2018年 / 12卷 / 06期
关键词：
robust control; time-varying systems; Lyapunov methods; uncertain systems; delays; linear matrix inequalities; stability criteria; approximation theory; stabilisation; delay-dependent stability; uncertain delta operator systems; three-term approximation; stability criterion; delay-dependent robust stability; time-varying delays; approximation error; model transformation; scaled small gain; appropriate Lyapunov-Krasovskii functional; H-INFINITY CONTROL; CRITERIA; LYAPUNOV; BOUNDS; MODEL;
D O I：
10.1049/iet-cta.2017.0006
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 study investigates the problem of delay-dependent stability and stabilisation of uncertain delta operator systems with time-varying delay. A new model transformation is proposed using a three-term approximation, which has a smaller approximation error than the existing methods based on one or two terms. On the basis of scaled small gain theorem (scaled small gain) and an appropriate Lyapunov-Krasovskii functional, a new stability criterion is proposed in terms of linear matrix inequalities. Finally, numerical examples are presented to illustrate the effectiveness of the proposed method.
引用
收藏
页码：786 / 792
页数：7
相关论文
共 33 条
  • [1] Optimising stability bounds of finite-precision controller structures for sampled-data systems in the δ-operator domain
    Chen, S
    Wu, J
    Istepanian, RH
    Chu, J
    Whidborne, JF
    [J]. IEE PROCEEDINGS-CONTROL THEORY AND APPLICATIONS, 1999, 146 (06): : 517 - 526
  • [2] Input-output approach to stability and L2-gain analysis of systems with time-varying delays
    Fridman, Emilia
    Shaked, Uri
    [J]. SYSTEMS & CONTROL LETTERS, 2006, 55 (12) : 1041 - 1053
  • [3] GAHINET P, 1994, IEEE DECIS CONTR P, P2038, DOI 10.1109/CDC.1994.411440
  • [4] RAPPROCHEMENT BETWEEN CONTINUOUS AND DISCRETE MODEL-REFERENCE ADAPTIVE-CONTROL
    GOODWIN, GC
    LEAL, RL
    MAYNE, DQ
    MIDDLETON, RH
    [J]. AUTOMATICA, 1986, 22 (02) : 199 - 207
  • [5] Small gain problem in coupled differential-difference equations, time-varying delays, and direct Lyapunov method
    Gu, Kegin
    Zhang, Yashun
    Xu, Shengyuan
    [J]. INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, 2011, 21 (04) : 429 - 451
  • [6] An integral inequality in the stability problem of time-delay systems
    Gu, KQ
    [J]. PROCEEDINGS OF THE 39TH IEEE CONFERENCE ON DECISION AND CONTROL, VOLS 1-5, 2000, : 2805 - 2810
  • [7] THE ZEROS AND POLES OF DELTA-OPERATOR SYSTEMS
    HERSH, MA
    [J]. INTERNATIONAL JOURNAL OF CONTROL, 1993, 57 (03) : 557 - 575
  • [8] Hmamed A, 2015, IEEE DECIS CONTR P, P1756, DOI 10.1109/CDC.2015.7402464
  • [9] Hmamed A., 2006, ISCCSP 2 INT S COMM, P13
  • [10] Hmamed A., 2007, CSC C SYST CONTR MAR, P16
1234