Feedback Stabilization of First Order Neutral Delay Systems Using the Lambert W Function

Feedback Stabilization of First Order Neutral Delay Systems Using the Lambert W Function

This paper presents a new approach to stabilize the first order neutral delay differential systems with two time delays. First, we provided a few oscillation and non-oscillation criteria for the neutral delay differential equations using spectrum analysis and the Lambert W function. These conditions...

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Main Authors: Beomsoo Kim, Jaesung Kwon, Sungwoong Choi, Jeonghyeon Yang
Format: Article
Language:English
Published: MDPI AG 2019-08-01
Series:Applied Sciences
Subjects:
neutral delay systems
oscillation
stabilization
feedback control
Lambert W function
Online Access:https://www.mdpi.com/2076-3417/9/17/3539
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spelling doaj-f2afb10670c14f51aeb2f9bfb9b031a52020-11-24T20:52:50ZengMDPI AGApplied Sciences2076-34172019-08-01917353910.3390/app9173539app9173539Feedback Stabilization of First Order Neutral Delay Systems Using the Lambert W FunctionBeomsoo Kim0Jaesung Kwon1Sungwoong Choi2Jeonghyeon Yang3Department of Mechanical System Engineering, Gyeongsang National University, Tongyeong 53064, KoreaDepartment of Mechanical System Engineering, Gyeongsang National University, Tongyeong 53064, KoreaDepartment of Mechanical System Engineering, Gyeongsang National University, Tongyeong 53064, KoreaDepartment of Mechanical System Engineering, Gyeongsang National University, Tongyeong 53064, KoreaThis paper presents a new approach to stabilize the first order neutral delay differential systems with two time delays. First, we provided a few oscillation and non-oscillation criteria for the neutral delay differential equations using spectrum analysis and the Lambert W function. These conditions were explicit and the real roots were analytically expressed in terms of the Lambert W function in the case of non-oscillation. Second, we designed a stabilizing state feedback controller for the neutral delay differential systems with two time delays, wherein the proportional and derivative gains were analytically determined using the results of the non-oscillation criteria. A few examples are given to illustrate the main results.https://www.mdpi.com/2076-3417/9/17/3539neutral delay systemsoscillationstabilizationfeedback controlLambert W function
collection DOAJ
language English
format Article
sources DOAJ
author Beomsoo Kim
Jaesung Kwon
Sungwoong Choi
Jeonghyeon Yang
spellingShingle Beomsoo Kim
Jaesung Kwon
Sungwoong Choi
Jeonghyeon Yang
Feedback Stabilization of First Order Neutral Delay Systems Using the Lambert W Function
Applied Sciences
neutral delay systems
oscillation
stabilization
feedback control
Lambert W function
author_facet Beomsoo Kim
Jaesung Kwon
Sungwoong Choi
Jeonghyeon Yang
author_sort Beomsoo Kim
title Feedback Stabilization of First Order Neutral Delay Systems Using the Lambert W Function
title_short Feedback Stabilization of First Order Neutral Delay Systems Using the Lambert W Function
title_full Feedback Stabilization of First Order Neutral Delay Systems Using the Lambert W Function
title_fullStr Feedback Stabilization of First Order Neutral Delay Systems Using the Lambert W Function
title_full_unstemmed Feedback Stabilization of First Order Neutral Delay Systems Using the Lambert W Function
title_sort feedback stabilization of first order neutral delay systems using the lambert w function
publisher MDPI AG
series Applied Sciences
issn 2076-3417
publishDate 2019-08-01
description This paper presents a new approach to stabilize the first order neutral delay differential systems with two time delays. First, we provided a few oscillation and non-oscillation criteria for the neutral delay differential equations using spectrum analysis and the Lambert W function. These conditions were explicit and the real roots were analytically expressed in terms of the Lambert W function in the case of non-oscillation. Second, we designed a stabilizing state feedback controller for the neutral delay differential systems with two time delays, wherein the proportional and derivative gains were analytically determined using the results of the non-oscillation criteria. A few examples are given to illustrate the main results.
topic neutral delay systems
oscillation
stabilization
feedback control
Lambert W function
url https://www.mdpi.com/2076-3417/9/17/3539
work_keys_str_mv AT beomsookim feedbackstabilizationoffirstorderneutraldelaysystemsusingthelambertwfunction
AT jaesungkwon feedbackstabilizationoffirstorderneutraldelaysystemsusingthelambertwfunction
AT sungwoongchoi feedbackstabilizationoffirstorderneutraldelaysystemsusingthelambertwfunction
AT jeonghyeonyang feedbackstabilizationoffirstorderneutraldelaysystemsusingthelambertwfunction
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