A several complex variables approach to feedback stabilization of linear neutral delay-differential systems

1984 ◽  
Vol 17 (1) ◽  
pp. 97-133 ◽  
Author(s):  
Christopher I. Byrnes ◽  
Mark W. Spong ◽  
Tzyh-Jong Tarn
Keyword(s):  
Complex Variables ◽  
Feedback Stabilization ◽  
Several Complex Variables ◽  
Neutral Delay ◽  
Differential Systems ◽  
Delay Differential Systems ◽  
Delay Differential

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

2019 ◽  
Vol 9 (17) ◽  
pp. 3539 ◽  
Author(s):  
Beomsoo Kim ◽  
Jaesung Kwon ◽  
Sungwoong Choi ◽  
Jeonghyeon Yang
Keyword(s):  
Time Delays ◽  
Feedback Stabilization ◽  
Delay Systems ◽  
Lambert W Function ◽  
Neutral Delay ◽  
Differential Systems ◽  
Oscillation Criteria ◽  
First Order ◽  
Delay Differential Systems ◽  
Delay Differential

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.

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