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Open AccessArticle

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

Department of Mechanical System Engineering, Gyeongsang National University, Tongyeong 53064, Korea
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Appl. Sci. 2019, 9(17), 3539; https://doi.org/10.3390/app9173539
Received: 9 July 2019 / Revised: 13 August 2019 / Accepted: 23 August 2019 / Published: 28 August 2019
(This article belongs to the Special Issue Artificial Intelligence for Smart Systems)
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. View Full-Text
Keywords: neutral delay systems; oscillation; stabilization; feedback control; Lambert W function neutral delay systems; oscillation; stabilization; feedback control; Lambert W function
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MDPI and ACS Style

Kim, B.; Kwon, J.; Choi, S.; Yang, J. Feedback Stabilization of First Order Neutral Delay Systems Using the Lambert W Function. Appl. Sci. 2019, 9, 3539.

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