First-order representation of delay-differential systems

2001 ◽  
Author(s):  
P. Vettori ◽  
S. Zampieri
Keyword(s):  
Differential Systems ◽  
First Order ◽  
Order Representation ◽  
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.

scholarly journals Delay-Dependent Stability, Integrability and Boundedeness Criteria for Delay Differential Systems

Axioms ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 138
Author(s):  
Osman Tunç ◽  
Cemil Tunç ◽  
Yuanheng Wang
Keyword(s):  
Multiple Time ◽  
Time Varying ◽  
Differential Systems ◽  
First Order ◽  
Uniformly Asymptotic Stability ◽  
Delay Differential Systems ◽  
The Stability ◽  
Delay Differential ◽  
Delay Dependent ◽  
Delay Dependent Stability

This paper deals with non-perturbed and perturbed systems of nonlinear differential systems of first order with multiple time-varying delays. Here, for the considered systems, easily verifiable and applicable uniformly asymptotic stability, integrability, and boundedness criteria are obtained via defining an appropriate Lyapunov–Krasovskiĭ functional (LKF) and using the Lyapunov– Krasovskiĭ method (LKM). Comparisons with a former result that can be found in the literature illustrate the novelty of the stability theorem and show new contributions to the qualitative theory of solutions. A discussion of two illustrative examples and the obtained results are presented.

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.

Sign in / Sign up

Export Citation Format

Share Document