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.

scholarly journals Equivalence and Reduction of Delay-Differential Systems

2007 ◽  
Vol 17 (1) ◽  
pp. 15-22 ◽  
Author(s):  
Mohamed Boudellioua
Keyword(s):  
Direct Method ◽  
Polynomial System ◽  
Original System ◽  
Neutral Delay ◽  
Differential Systems ◽  
First Order ◽  
Order Form ◽  
Delay Differential Systems ◽  
System Equivalence ◽  
Delay Differential

Equivalence and Reduction of Delay-Differential SystemsA new direct method is presented which reduces a given high-order representation of a control system with delays to a first-order form that is encountered in the study of neutral delay-differential systems. Using the polynomial system description (PMD) setting due to Rosenbrock, it is shown that the transformation connecting the original PMD with the first-order form is Fuhrmann's strict system equivalence. This type of system equivalence leaves the transfer function and other relevant structural properties of the original system invariant.

scholarly journals Oscillation Criteria of First Order Neutral Delay Differential Equations with Variable Coefficients

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Fatima N. Ahmed ◽  
Rokiah Rozita Ahmad ◽  
Ummul Khair Salma Din ◽  
Mohd Salmi Md Noorani
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Variable Coefficients ◽  
Neutral Delay ◽  
Oscillation Criteria ◽  
First Order ◽  
Neutral Delay Differential Equations ◽  
Delay Differential

Some new oscillation criteria are given for first order neutral delay differential equations with variable coefficients. Our results generalize and extend some of the well-known results in the literature. Some examples are considered to illustrate the main results.

Estimation of Time-Delays Using the Characteristic Roots of Delay Differential Equations

2011 ◽  
Author(s):  
Sun Yi ◽  
Sangseok Yu
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Time Delays ◽  
Delay Systems ◽  
Lambert W Function ◽  
Short Paper ◽  
Characteristic Roots ◽  
General Systems ◽  
Delay Differential ◽  
Estimation Of Time

In this short paper, the preliminary result of a new method for estimation of time-delays of time-delay systems is presented. The presented method makes use of the Lambert W function, and is for scalar first-order delay differential equations (DDEs). Possible extension to general systems of DDEs and application to physical systems are also discussed.

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