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...
Main Authors: | , |
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Format: | Article |
Language: | English |
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Texas State University
2000-02-01
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Series: | Electronic Journal of Differential Equations |
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Online Access: | http://ejde.math.txstate.edu/Volumes/2000/11/abstr.html |
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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 |