Robust feedback stabilization by means of Lyapunov-like functions determined by Lie brackets

被引：3

作者：

Fusco, Giovanni ^{[1
]}

机构：

[1] Univ Padua, Dept Math Tullio Levi Civita, Via Trieste 63, I-35121 Padua, Italy

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2021年 / 287卷

关键词：

Lyapunov functions; Asymptotic stabilizability; Robustness; Discontinuous feedback law; System sampling; Lie brackets; ASYMPTOTIC CONTROLLABILITY;

D O I：

10.1016/j.jde.2021.03.048

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We use Lie brackets of unbounded vector fields to consider a dissipative relation that generalizes the differential inequality which defines classic control Lyapunov functions. Under minimal regularity assumptions, we employ locally semiconcave solutions of this extended relation, called in the following degree-k control Lyapunov functions, in order to design degree-k Lyapunov feedbacks, i.e. particular discontinuous feedback laws that stabilize the underlying system to a given closed target with compact boundary, in the sample and hold sense. We also prove that this feedback construction is robust when small measurement errors and external disturbances occur. (C) 2021 Elsevier Inc. All rights reserved.

引用

页码：88 / 112

页数：25

共 50 条

[41] Universal stabilization using control lyapunov functions, adaptive derivative feedback and neural network approximators
Kosmatopoulos, EB
[J]. PROCEEDINGS OF THE 35TH IEEE CONFERENCE ON DECISION AND CONTROL, VOLS 1-4, 1996, : 2444 - 2449
[42] Universal stabilization using control Lyapunov functions, adaptive derivative feedback, and neural network approximators
Kosmatopoulos, EB
[J]. IEEE TRANSACTIONS ON SYSTEMS MAN AND CYBERNETICS PART B-CYBERNETICS, 1998, 28 (03): : 472 - 477
[43] PROBLEMS AT RESONANCE FOR 1ST AND 2ND ORDER DIFFERENTIAL-EQUATIONS VIA LYAPUNOV-LIKE FUNCTIONS
NIETO, JJ
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1983, 7 (01) : 61 - 69
[44] Robust stabilization and enlargement of attractive region of control systems using piecewise linear Lyapunov functions
Ohta, Y
Takenaka, K
Fukuta, N
[J]. IECON'03: THE 29TH ANNUAL CONFERENCE OF THE IEEE INDUSTRIAL ELECTRONICS SOCIETY, VOLS 1 - 3, PROCEEDINGS, 2003, : 1140 - 1145
[45] Robust H∞ control and stabilization of uncertain switched linear systems:: A multiple Lyapunov functions approach
Ji, Zhijian
Guo, Xiaoxia
Wang, Long
Xie, Guangming
[J]. JOURNAL OF DYNAMIC SYSTEMS MEASUREMENT AND CONTROL-TRANSACTIONS OF THE ASME, 2006, 128 (03): : 696 - 700
[46] Convergence and stability analysis of system of partial differential equations under Markovian structural perturbations-I: Vector Lyapunov-like functions
Anabtawi, MJ
Ladde, GS
[J]. STOCHASTIC ANALYSIS AND APPLICATIONS, 2000, 18 (04) : 493 - 524
[47] Ito-Type Stochastic Parabolic Partial Differential Equations in Hilbert Spaces: Stability and Convergence Results via Lyapunov-Like Functions
Anabtawi, Mahmoud
Sathananthan, S.
[J]. STOCHASTIC ANALYSIS AND APPLICATIONS, 2011, 29 (05) : 749 - 768
[48] Finite-time stability and stabilization of singular state-delay systems using improved estimation of a lower bound on a Lyapunov-like functional
Stojanovic, S. B.
Debeljkovic, D. Lj.
Antic, D. S.
[J]. BULLETIN OF THE POLISH ACADEMY OF SCIENCES-TECHNICAL SCIENCES, 2015, 63 (02) : 479 - 487
[49] Robust nonlinear-nonquadratic feedback control via parameter-dependent Lyapunov functions
Haddad, WM
Chellaboina, VS
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1997, 30 (06) : 3725 - 3736
[50] Robust nonlinear-nonquadratic feedback control via parameter-dependent Lyapunov functions
Haddad, WM
Chellaboina, VS
[J]. INTERNATIONAL JOURNAL OF CONTROL, 1997, 66 (06) : 843 - 861

← 1 2 3 4 5 →