American Journal of Applied Sciences

Time-Delay Estimation using the Characteristic Roots of Delay Differential Equations

Sun Yi, Wonchang Choi and Taher Abu-Lebdeh

DOI : 10.3844/ajassp.2012.955.960

American Journal of Applied Sciences

Volume 9, Issue 6

Pages 955-960


Problem statement: For ordinary dynamic systems (i.e., non-delayed), various methods such as linear least-squares, gradient-weighted least-squares, Kalman filtering and other robust techniques have been widely used in signal processing, robotics, civil engineering. On the other hand, time-delay estimation of systems with unknown time-delay is still a challenging problem due to difficulty in formulation caused. Approach: The presented method makes use of the Lambert W function and analytical solutions of scalar first-order Delay Differential Equations (DDEs). The Lambert W function has been known to be useful in solving delay differential equations. From the solutions in terms of the Lambert W function, the dominant characteristic roots can be obtained and used to estimate time-delays. The function is already embedded in various software packages (e.g., MATLAB) and thus, the presented method can be readily used for time-delay systems. Results: The presented method and the provided examples show ease of formulation and accuracy of time-delay estimation. Conclusion: Estimation of time-delays can be conducted in an analytical way. The presented method will be extended to general systems of DDEs and application to physical systems.


© 2012 Sun Yi, Wonchang Choi and Taher Abu-Lebdeh. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.