Levant's Arbitrary-Order Exact Differentiator: A Lyapunov Approach

被引：104
作者：
Cruz-Zavala, Emmanuel [1 ]
Moreno, Jaime A. [2 ]
机构：
[1] Univ Guadalajara, Ctr Univ Ciencias Exactas & Ingn, Dept Comp Sci, Guadalajara 44430, Jalisco, Mexico
[2] Univ Nacl Autonoma Mexico, Inst Ingn, Mexico City 04510, DF, Mexico
来源：
IEEE TRANSACTIONS ON AUTOMATIC CONTROL | 2019年 / 64卷 / 07期
关键词：
Nonlinear systems; observers; sliding mode control; RECURSIVE OBSERVER DESIGN; FINITE-TIME; HOMOGENEOUS APPROXIMATION; NONLINEAR-SYSTEMS; STABILIZATION;
D O I：
10.1109/TAC.2018.2874721
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
We propose a family of smooth explicit Lyapunov functions (LF) for Levant's differentiator, which is a discontinuous real-time robust and exact differentiator. These LF allow the analysis of the convergence and performance properties and the design of appropriate gains for the differentiator.
引用
收藏
页码：3034 / 3039
页数：6
相关论文
共 26 条
  • [1] Homogeneous approximation, recursive observer design, and output feedback
    Andrieu, Vincent
    Praly, Laurent
    Astolfi, Alessandro
    [J]. SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2008, 47 (04) : 1814 - 1850
  • [2] [Anonymous], 2000, Journal of Signal Processing
  • [3] Bacciotti A., 2005, Liapunov Functions and Stability in Control Theory, Vsecond
  • [4] Finite- and fixed-time differentiators utilising HOSM techniques
    Basin, Michael
    Yu, Polk
    Shtessel, Yuri
    [J]. IET CONTROL THEORY AND APPLICATIONS, 2017, 11 (08) : 1144 - 1152
  • [5] On homogeneity and its application in sliding mode control
    Bernuau, Emmanuel
    Efimov, Denis
    Perruquetti, Wilfrid
    Polyakov, Andrey
    [J]. JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS, 2014, 351 (04): : 1866 - 1901
  • [6] Geometric homogeneity with applications to finite-time stability
    Bhat, SP
    Bernstein, DS
    [J]. MATHEMATICS OF CONTROL SIGNALS AND SYSTEMS, 2005, 17 (02) : 101 - 127
  • [7] Second-order sliding-mode observer for mechanical systems
    Davila, J
    Fridman, L
    Levant, A
    [J]. IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2005, 50 (11) : 1785 - 1789
  • [8] Nonsmooth stabilization of a class of nonlinear cascaded systems
    Ding, Shihong
    Li, Shihua
    Zheng, Wei Xing
    [J]. AUTOMATICA, 2012, 48 (10) : 2597 - 2606
  • [9] A Hybrid Robust Non-Homogeneous Finite-Time Differentiator
    Efimov, Denis V.
    Fridman, Leonid
    [J]. IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2011, 56 (05) : 1213 - 1219
  • [10] Filippov A. F., 1988, Math. Appl. (Soviet Series), P1
123