Finite-time and fixed-time input-to-state stability: Explicit and implicit approaches

被引：38
作者：
Lopez-Ramirez, Francisco [1 ]
Efimov, Denis [1 ,2 ]
Polyakov, Andrey [1 ,2 ]
Perruquetti, Wilfrid [3 ]
机构：
[1] Univ Lille, CNRS, INRIA, UMR 9189,CRIStAL, F-59000 Lille, France
[2] ITMO Univ, 49 Kronverkskiy Av, St Petersburg 197101, Russia
[3] Ecole Cent Lille, CNRS, Cite Sci, UMR 9189,CRIStAL, F-59651 Villeneuve Dascq, France
来源：
SYSTEMS & CONTROL LETTERS | 2020年 / 144卷
关键词：
Finite-Time Stability; Fixed-Time Stability; Input-to-State Stability; STABILIZATION; DESIGN; DISCRETIZATION; HOMOGENEITY;
D O I：
10.1016/j.sysconle.2020.104775
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 present article gathers the analysis of non-asymptotic convergence rates (finite-time and fixedtime) with the property of input-to-state stability. Theoretical tools to determine this joint property are presented for the case where an explicit ISS Lyapunov function is known, and when it remains in implicit form (e.g. as a solution of an algebraic equation). For the case of finite-time input-to-state stability, necessary and sufficient conditions are given whereas for the fixed-time case only a sufficient condition is obtained. Academic examples and numerical simulations support the obtained results. (C) 2020 Elsevier B.V. All rights reserved.
引用
收藏
页数：9
相关论文
共 34 条
[1]   A class of robust consensus algorithms with predefined-time convergence under switching topologies [J].
Aldana-Lopez, Rodrigo ;
Gomez-Gutierrez, David ;
Defoort, Michael ;
Diego Sanchez-Torres, Juan ;
Jonathan Munoz-Vazquez, Aldo .
INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, 2019, 29 (17) :6179-6198
[2]   Enhancing the settling time estimation of a class of fixed-time stable systems [J].
Aldana-Lopez, Rodrigo ;
Gomez-Gutierrez, David ;
Jimenez-Rodriguez, Esteban ;
Diego Sanchez-Torres, Juan ;
Defoort, Michael .
INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, 2019, 29 (12) :4135-4148
[3]  
Bacciotti A., 2005, Lyapunov Functions and Stability in Control Theory
[4]   Continuous finite-time stabilization of the translational and rotational double integrators [J].
Bhat, SP ;
Bernstein, DS .
IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 1998, 43 (05) :678-682
[5]   Finite-time stability of continuous autonomous systems [J].
Bhat, SP ;
Bernstein, DS .
SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2000, 38 (03) :751-766
[6]   Geometric homogeneity with applications to finite-time stability [J].
Bhat, SP ;
Bernstein, DS .
MATHEMATICS OF CONTROL SIGNALS AND SYSTEMS, 2005, 17 (02) :101-127
[7]   Uniform Robust Exact Differentiator [J].
Cruz-Zavala, Emmanuel ;
Moreno, Jaime A. ;
Fridman, Leonid M. .
IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2011, 56 (11) :2727-2733
[8]   Input to State Stability and Allied System Properties [J].
Dashkovskiy, S. N. ;
Efimov, D. V. ;
Sontag, E. D. .
AUTOMATION AND REMOTE CONTROL, 2011, 72 (08) :1579-1614
[9]   A New Second-Order Sliding Mode and Its Application to Nonlinear Constrained Systems [J].
Ding, Shihong ;
Mei, Keqi ;
Li, Shihua .
IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2019, 64 (06) :2545-2552
[10]  
Edwards C., 1998, Sliding Mode Control
1234