Finite-time input-to-state stability and applications to finite-time control design

Yiguang Hong, Zhong-Ping Jiang, Gang Feng

Research output: Contribution to journalArticle

Abstract

This paper extends the well-known concept, Sontag's input-to-state stability (ISS), to finite-time control problems. In other words, a new concept, finite-time input-to-state stability (FTISS), is proposed and then is applied to both the analysis of finite-time stability and the design of finite-time stabilizing feedback laws of control systems. With finite-time stability, nonsmoothness has to be considered, and serious technical challenges arise in the design of finite-time controllers and the stability analysis of the closed-loop system. It is found that FTISS plays an important role as the conventional ISS in the context of asymptotic stability analysis and smooth feedback stabilization. Moreover, a robust adaptive controller is proposed to handle nonlinear systems with parametric and dynamic uncertainties by virtue of FTISS and related arguments.

Original languageEnglish (US)
Pages (from-to)4395-4418
Number of pages24
JournalSIAM Journal on Control and Optimization
Volume48
Issue number7
DOIs
StatePublished - 2010

Fingerprint

Finite-time Stability
Control Design
Stability Analysis
Controller
Feedback Law
Feedback Stabilization
Asymptotic Analysis
Asymptotic Stability
Closed-loop System
Control Problem
Feedback
Nonlinear Systems
Controllers
Control System
Uncertainty
Asymptotic stability
Closed loop systems
Nonlinear systems
Stabilization
Control systems

Keywords

  • Finite-time control
  • Input-to-state stability
  • Lyapunov functions
  • Nonsmooth feedback
  • Uncertainties

ASJC Scopus subject areas

  • Control and Optimization
  • Applied Mathematics

Cite this

Finite-time input-to-state stability and applications to finite-time control design. / Hong, Yiguang; Jiang, Zhong-Ping; Feng, Gang.

In: SIAM Journal on Control and Optimization, Vol. 48, No. 7, 2010, p. 4395-4418.

Research output: Contribution to journalArticle

@article{a418a156c346417d85c06c9f1e48ae3c,
title = "Finite-time input-to-state stability and applications to finite-time control design",
abstract = "This paper extends the well-known concept, Sontag's input-to-state stability (ISS), to finite-time control problems. In other words, a new concept, finite-time input-to-state stability (FTISS), is proposed and then is applied to both the analysis of finite-time stability and the design of finite-time stabilizing feedback laws of control systems. With finite-time stability, nonsmoothness has to be considered, and serious technical challenges arise in the design of finite-time controllers and the stability analysis of the closed-loop system. It is found that FTISS plays an important role as the conventional ISS in the context of asymptotic stability analysis and smooth feedback stabilization. Moreover, a robust adaptive controller is proposed to handle nonlinear systems with parametric and dynamic uncertainties by virtue of FTISS and related arguments.",
keywords = "Finite-time control, Input-to-state stability, Lyapunov functions, Nonsmooth feedback, Uncertainties",
author = "Yiguang Hong and Zhong-Ping Jiang and Gang Feng",
year = "2010",
doi = "10.1137/070712043",
language = "English (US)",
volume = "48",
pages = "4395--4418",
journal = "SIAM Journal on Control and Optimization",
issn = "0363-0129",
publisher = "Society for Industrial and Applied Mathematics Publications",
number = "7",

}

TY - JOUR

T1 - Finite-time input-to-state stability and applications to finite-time control design

AU - Hong, Yiguang

AU - Jiang, Zhong-Ping

AU - Feng, Gang

PY - 2010

Y1 - 2010

N2 - This paper extends the well-known concept, Sontag's input-to-state stability (ISS), to finite-time control problems. In other words, a new concept, finite-time input-to-state stability (FTISS), is proposed and then is applied to both the analysis of finite-time stability and the design of finite-time stabilizing feedback laws of control systems. With finite-time stability, nonsmoothness has to be considered, and serious technical challenges arise in the design of finite-time controllers and the stability analysis of the closed-loop system. It is found that FTISS plays an important role as the conventional ISS in the context of asymptotic stability analysis and smooth feedback stabilization. Moreover, a robust adaptive controller is proposed to handle nonlinear systems with parametric and dynamic uncertainties by virtue of FTISS and related arguments.

AB - This paper extends the well-known concept, Sontag's input-to-state stability (ISS), to finite-time control problems. In other words, a new concept, finite-time input-to-state stability (FTISS), is proposed and then is applied to both the analysis of finite-time stability and the design of finite-time stabilizing feedback laws of control systems. With finite-time stability, nonsmoothness has to be considered, and serious technical challenges arise in the design of finite-time controllers and the stability analysis of the closed-loop system. It is found that FTISS plays an important role as the conventional ISS in the context of asymptotic stability analysis and smooth feedback stabilization. Moreover, a robust adaptive controller is proposed to handle nonlinear systems with parametric and dynamic uncertainties by virtue of FTISS and related arguments.

KW - Finite-time control

KW - Input-to-state stability

KW - Lyapunov functions

KW - Nonsmooth feedback

KW - Uncertainties

UR - http://www.scopus.com/inward/record.url?scp=77958540045&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77958540045&partnerID=8YFLogxK

U2 - 10.1137/070712043

DO - 10.1137/070712043

M3 - Article

VL - 48

SP - 4395

EP - 4418

JO - SIAM Journal on Control and Optimization

JF - SIAM Journal on Control and Optimization

SN - 0363-0129

IS - 7

ER -