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

被引：34
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.
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页数：9
相关论文
共 34 条
  • [21] Lopez-Ramirez F, 2018, IEEE DECIS CONTR P, P706, DOI 10.1109/CDC.2018.8619502
  • [22] Conditions for fixed-time stability and stabilization of continuous autonomous systems
    Lopez-Ramirez, Francisco
    Efimov, Denis
    Polyakov, Andrey
    Perruquetti, Wilfrid
    [J]. SYSTEMS & CONTROL LETTERS, 2019, 129 : 26 - 35
  • [23] Finite-time and fixed-time observer design: Implicit Lyapunov function approach
    Lopez-Ramirez, Francisco
    Polyakov, Andrey
    Efimov, Denis
    Perruquetti, Wilfrid
    [J]. AUTOMATICA, 2018, 87 : 52 - 60
  • [24] Nakamura H, 2002, SICE 2002: PROCEEDINGS OF THE 41ST SICE ANNUAL CONFERENCE, VOLS 1-5, P1974, DOI 10.1109/SICE.2002.1196633
  • [25] Nakamura H., 2007, IFAC P VOLUMES, V40, P1120
  • [26] CONSISTENT DISCRETIZATION OF FINITE-TIME AND FIXED-TIME STABLE SYSTEMS
    Polyakov, Andrey
    Efimov, Denis
    Brogliato, Bernard
    [J]. SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2019, 57 (01) : 78 - 103
  • [27] Finite-time and fixed-time stabilization: Implicit Lyapunov function approach
    Polyakov, Andrey
    Efimov, Denis
    Perruquetti, Wilfrid
    [J]. AUTOMATICA, 2015, 51 : 332 - 340
  • [28] Stability notions and Lyapunov functions for sliding mode control systems
    Polyakov, Andrey
    Fridman, Leonid
    [J]. JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS, 2014, 351 (04): : 1831 - 1865
  • [29] Nonlinear Feedback Design for Fixed-Time Stabilization of Linear Control Systems
    Polyakov, Andrey
    [J]. IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2012, 57 (08) : 2106 - U1
  • [30] Roxin E., 1966, REND CIRC MAT PALERM, V15, P273, DOI DOI 10.1007/BF02844106
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