Converse Lyapunov theorems for control systems with unbounded controls

被引：2

作者：

Lai, Anna Chiara ^{[1
]}

Motta, Monica ^{[2
]}

机构：

[1] Sapienza Univ Roma, Dipartimento Sci Base & Applicate Ingn, Via Antonio Scarpa 10, I-00161 Rome, Italy

[2] Univ Padua, Dipartimento Matemat Tullio Levi Civita, Via Trieste 63, I-35121 Padua, Italy

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2022年 / 312卷

关键词：

Converse Lyapunov theorem; Asymptotic controllability; Asymptotic stabilizability; Discontinuous feedback law; Impulsive control systems; L-1 LIMIT SOLUTIONS; ASYMPTOTIC CONTROLLABILITY; FEEDBACK STABILIZATION; STABILIZABILITY; EXTENSION; STABILITY; LIPSCHITZ; INPUT;

D O I：

10.1016/j.jde.2021.12.022

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we extend well-known relationships between global asymptotic controllability, sample stabilizability, and the existence of a control Lyapunov function to a wide class of control systems with unbounded controls, including control-polynomial systems. In particular, we consider open loop controls and discontinuous stabilizing feedbacks, which may be unbounded approaching the target, so that the corresponding trajectories may present a chattering behaviour. A key point of our results is to prove that global asymptotic controllability, sample stabilizability, and existence of a control Lyapunov function for these systems or for an impulsive extension of them are equivalent. (c) 2021 Elsevier Inc. All rights reserved.

引用

页码：347 / 373

页数：27

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