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Mathematical Problems in Engineering
Volume 2013, Article ID 658194, 18 pages
Research Article

Online Identification of Multivariable Discrete Time Delay Systems Using a Recursive Least Square Algorithm

National Engineering school of Gabes, Numerical Control of Industrial Processes Research Unit, Gabes University, Route de Medenine, BP 6029, Gabes, Tunisia

Received 6 February 2013; Revised 30 April 2013; Accepted 25 May 2013

Academic Editor: Yang Yi

Copyright © 2013 Saïda Bedoui et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper addresses the problem of simultaneous identification of linear discrete time delay multivariable systems. This problem involves both the estimation of the time delays and the dynamic parameters matrices. In fact, we suggest a new formulation of this problem allowing defining the time delay and the dynamic parameters in the same estimated vector and building the corresponding observation vector. Then, we use this formulation to propose a new method to identify the time delays and the parameters of these systems using the least square approach. Convergence conditions and statistics properties of the proposed method are also developed. Simulation results are presented to illustrate the performance of the proposed method. An application of the developed approach to compact disc player arm is also suggested in order to validate simulation results.