Survey on Analysis of Time Delayed Systems via the Lambert W Function
@inproceedings{Yi2007SurveyOA, title={Survey on Analysis of Time Delayed Systems via the Lambert W Function}, author={Sun Yi and Patrick W. Nelson and Ali Galip Ulsoy}, year={2007} }
This paper summarizes recent research on an approach for the analytical solution to systems of delay differential equations developed using the Lambert W function [26, 29], and its applications [25, 28]. Also, several outstanding research problems associated with the solution of systems of delay differential equations using the matrix Lambert W function are highlighted. The solution has the form of an infinite series of modes written in terms of the matrix Lambert W function. The essential…
No Paper Link Available
34 Citations
Analysis and Control of Time Delayed Systems via the Lambert W Function ?
- Mathematics
- 2008
This paper summarizes recent research results by the authors for the analytical solution to systems of delay differential equations using the matrix Lambert W function, and its applications to…
The Use of the Lambert Function Method for Analysis of a Control System with Delays
- MathematicsInf. Technol. Control.
- 2013
The mathematical model of the mutual synchronization system with complete graph structure, composed of n (n∈N) oscillators, is investigated and the step responses matrix of the synchronization system is defined and the transients in the system are investigated.
Solutions of neutral delay differential equations using a generalized Lambert W function
- MathematicsAppl. Math. Comput.
- 2020
Analysis of higher order time delay systems using Lambert W function
- MathematicsArXiv
- 2016
A new class of time delay systems is characterized to extend the applicability of the above said method and a state variable transformation is used to transform the proposed class of systems into the common canonical form.
Some results of finding the roots of time-delay systems by Lambert W function
- Mathematics2021 IEEE International Conference on Power Electronics, Computer Applications (ICPECA)
- 2021
A unified formula is used to find the roots of the transcendental characteristic equations for both an integer and fractional -order time delay systems by using Lambert W function solutions. However,…
Controllability and Observability of Systems of Linear Delay Differential Equations via the Matrix Lambert W Function
- Mathematics2007 American Control Conference
- 2007
The criteria for controllability and observability, and their Gramians, for systems of delay differential equations using the solution in terms of the matrix Lambert W function are presented for the first time and illustrated with examples.
Eigenvalue Assignment via the Lambert W Function for Control of Time-delay Systems
- Mathematics, Computer Science
- 2010
This paper considers the problem of feedback controller design via eigenvalue assignment for linear time-invariant systems of linear delay differential equations (DDEs) with a single delay, and presents an analytical form expressed in terms of the parameters of the DDE, similar to the state transition matrix in linear ODEs.
Robust control and time-domain specifications for systems of delay differential equations via eigenvalue assignment
- Mathematics2008 American Control Conference
- 2008
An approach for eigenvalue assignment for systems of delay differential equations (DDEs), based upon the Lambert W function, is applied to the problem of robust control design for perturbed systems…
Spurious roots of delay differential equations using Galerkin approximations
- Mathematics, Computer Science
- 2020
It is demonstrated that the second-order Galerkin method produces spurious roots near the origin, which must then be identified through substitution into the characteristic polynomial of the original delay differential equation, but spurious roots do not arise if the first- order Galerkins method is used, which can reduce computation time and simplify stability analyses.
References
SHOWING 1-10 OF 33 REFERENCES
Solution of a system of linear delay differential equations using the matrix Lambert function
- Mathematics2006 American Control Conference
- 2006
An approach for the analytical solution to systems of delay differential equations (DDEs) has been developed using the matrix Lambert function. To generalize the Lambert function method for scalar…
Analysis of Systems of Linear Delay Differential Equations Using the Matrix Lambert Function and the Laplace Transformation
- Mathematics
- 2006
An approach for the analytical solution, free and forced, to systems of delay differential equations (DDEs) has been developed using the matrix Lambert function. To generalize the Lambert function…
Analysis of a System of Linear Delay Differential Equations
- Mathematics
- 2003
A new analytic approach to obtain the complete solution for systems of delay differential equations (DDE) based on the concept of Lambert functions is presented. The similarity with the concept of…
Solution of Systems of Linear Delay Differential Equations via Laplace Transformation
- MathematicsProceedings of the 45th IEEE Conference on Decision and Control
- 2006
The analytical solution is utilized to present a solution in the Laplace domain, present validation examples, and emphasize the analogy of the solution method to systems of ordinary differential equations.
Chatter Stability Analysis Using the Matrix Lambert Function and Bifurcation Analysis
- Mathematics
- 2006
We investigate the stability of the regenerative machine tool chatter problem, in a turning process modeled using delay differential equations (DDEs). An approach using the matrix Lambert function…
Robust stability analysis of linear time-delay systems by Lambert W function: Some extreme point results
- MathematicsAutom.
- 2006
FEEDBACK CONTROL VIA EIGENVALUE ASSIGNMENT FOR TIME DELAYED SYSTEMS USING THE LAMBERT W FUNCTION
- Mathematics
- 2007
In this paper, we consider the problem of feedback controller design via eigenvalue assignment for systems of linear delay differential equations (DDEs). Unlike ordinary differential equations…
Direct stability boundary method for distributed systems with discrete delay
- Mathematics
- 1988
The distributed systems considered are those with a characteristic equation expressed in terms of u = √s, where s is the usual Laplace transform variable. The discrete delay h enters the…
Analysis and Synthesis of Time Delay Systems
- Mathematics
- 1989
This book gives emphasis to methods and results which are applicable to analysis and synthesis of industrial control systems with time delays, and is designed for those with knowledge of mathematical methods of control theory.
Time-delay systems: an overview of some recent advances and open problems
- Computer ScienceAutom.
- 2003