Implicit Lyapunov-Krasovski Functionals for Stability Analysis and Control Design of Time-Delay Systems

被引：37
作者：
Polyakov, Andrey [1 ,2 ]
Efimov, Denis [1 ,3 ]
Perruquetti, Wilfrid [1 ,2 ]
Richard, J-P. [1 ,2 ]
机构：
[1] Inria Lille Nord Europe, Non A, F-59650 Villeneuve Dascq, France
[2] CRIStAL CNRS UMR 9189 Ecole Cent Lille, F-59651 Villeneuve Dascq, France
[3] St Petersburg State Univ Informat Technol Mech &, Dept Control Syst & Informat, St Petersburg 197101, Russia
来源：
IEEE TRANSACTIONS ON AUTOMATIC CONTROL | 2015年 / 60卷 / 12期
关键词：
Delay systems; nonlinear control systems; STABILIZATION;
D O I：
10.1109/TAC.2015.2422451
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
The method of Implicit Lyapunov-Krasovski Functional (ILKF) for stability analysis of time-delay systems is introduced. Theorems on Lyapunov, asymptotic, (hyper) exponential, finite-time and fixed-time stability analysis using ILKF are presented. The hyper exponential stabilization algorithm for a time-delay system is presented. The theoretical result is supported by numerical simulation.
引用
收藏
页码：3344 / 3349
页数：6
相关论文
共 26 条
  • [1] Soft variable-structure controls: a survey
    Adamy, J
    Flemming, A
    [J]. AUTOMATICA, 2004, 40 (11) : 1821 - 1844
  • [2] [Anonymous], 1977, Applied Mathematical Sciences
  • [3] [Anonymous], 2005, Lyapunov Functions and Stability in Control Theory
  • [4] Finite-time stability of continuous autonomous systems
    Bhat, SP
    Bernstein, DS
    [J]. SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2000, 38 (03) : 751 - 766
  • [5] Bifurcations of equilibrium sets in mechanical systems with dry friction
    Biemond, J. J. Benjamin
    van de Wouw, Nathan
    Nijmeijer, Henk
    [J]. PHYSICA D-NONLINEAR PHENOMENA, 2012, 241 (22) : 1882 - 1894
  • [6] Finite-time convergent gradient flows with applications to network consensus
    Cortés, Jorge
    [J]. AUTOMATICA, 2006, 42 (11) : 1993 - 2000
  • [7] Courant R., 2000, Introduction to calculus and analysis, VII/1
  • [8] Driver Bruce K., 2003, Analysis Tools with Applications
  • [9] Efimov D., 2014, AUTOMATICA, DOI [10.1016/j.automatica.2014.05.010, DOI 10.1016/J.AUT0MATICA.2014.05.010]
  • [10] Descriptor discretized Lyapunov functional method: Analysis and design
    Fridman, Emilia
    [J]. IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2006, 51 (05) : 890 - 897
123