Asymptotic stability of nonlinear control systems described by difference equations with multiple delays

In this paper we study nonlinear control systems with multiple delays on controls and states. To obtain asymptotic stability, we impose Holder-type assumptions on the perturbing function, and show a Gronwall-type inequality for difference equations with delay. We prove that a nonlinear control syste...

Full description

Bibliographic Details
Main Authors: P. Niamsup, Vu Ngoc Phat
Format: Article
Language:English
Published: Texas State University 2000-02-01
Series:Electronic Journal of Differential Equations
Subjects:
Online Access:http://ejde.math.txstate.edu/Volumes/2000/11/abstr.html
_version_ 1818029253479890944
author P. Niamsup
Vu Ngoc Phat
author_facet P. Niamsup
Vu Ngoc Phat
author_sort P. Niamsup
collection DOAJ
description In this paper we study nonlinear control systems with multiple delays on controls and states. To obtain asymptotic stability, we impose Holder-type assumptions on the perturbing function, and show a Gronwall-type inequality for difference equations with delay. We prove that a nonlinear control system can be stabilized if its linear control system can be stabilized. Some examples are included in the last part of this paper.
first_indexed 2024-12-10T05:16:45Z
format Article
id doaj.art-24df00f75d2c4387aee1970d4a02b79f
institution Directory Open Access Journal
issn 1072-6691
language English
last_indexed 2024-12-10T05:16:45Z
publishDate 2000-02-01
publisher Texas State University
record_format Article
series Electronic Journal of Differential Equations
spelling doaj.art-24df00f75d2c4387aee1970d4a02b79f2022-12-22T02:00:56ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912000-02-01200011117Asymptotic stability of nonlinear control systems described by difference equations with multiple delaysP. NiamsupVu Ngoc PhatIn this paper we study nonlinear control systems with multiple delays on controls and states. To obtain asymptotic stability, we impose Holder-type assumptions on the perturbing function, and show a Gronwall-type inequality for difference equations with delay. We prove that a nonlinear control system can be stabilized if its linear control system can be stabilized. Some examples are included in the last part of this paper.http://ejde.math.txstate.edu/Volumes/2000/11/abstr.htmlStabilitydifference equationsnonlinear control systemsGronwall inequalityHolder conditionmultiple delay.
spellingShingle P. Niamsup
Vu Ngoc Phat
Asymptotic stability of nonlinear control systems described by difference equations with multiple delays
Electronic Journal of Differential Equations
Stability
difference equations
nonlinear control systems
Gronwall inequality
Holder condition
multiple delay.
title Asymptotic stability of nonlinear control systems described by difference equations with multiple delays
title_full Asymptotic stability of nonlinear control systems described by difference equations with multiple delays
title_fullStr Asymptotic stability of nonlinear control systems described by difference equations with multiple delays
title_full_unstemmed Asymptotic stability of nonlinear control systems described by difference equations with multiple delays
title_short Asymptotic stability of nonlinear control systems described by difference equations with multiple delays
title_sort asymptotic stability of nonlinear control systems described by difference equations with multiple delays
topic Stability
difference equations
nonlinear control systems
Gronwall inequality
Holder condition
multiple delay.
url http://ejde.math.txstate.edu/Volumes/2000/11/abstr.html
work_keys_str_mv AT pniamsup asymptoticstabilityofnonlinearcontrolsystemsdescribedbydifferenceequationswithmultipledelays
AT vungocphat asymptoticstabilityofnonlinearcontrolsystemsdescribedbydifferenceequationswithmultipledelays