Mathematical Problems in Engineering
Volume 2008 (2008), Article ID 270518, 15 pages
Research Article

Stabilization of Linear Sampled-Data Systems by a Time-Delay Feedback Control

F. Ricardo García,1,2 Baltazar Aguirre,2 and Rodolfo Suárez2

1UPIICSA-SEPI, Instituto Politécnico Nacional, Avenida Te 950, Mexico 08400, DF, Mexico
2Departamento de Matemáticas, Universidad Autónoma Metropolitana, San Rafael Atlixco 186, Mexico 09340, DF, Mexico

Received 4 August 2007; Revised 19 March 2008; Accepted 21 June 2008

Academic Editor: Tamas Kalmar-Nagy

Copyright © 2008 F. Ricardo García 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.


We consider one-dimensional, time-invariant sampled-data linear systems with constant feedback gain, an arbitrary fixed time delay, which is a multiple of the sampling period and a zero-order hold for reconstructing the sampled signal of the system in the feedback control. We obtain sufficient conditions on the coefficients of the characteristic polynomial associated with the system. We get these conditions by finding both lower and upper bounds on the coefficients. These conditions let us give both an estimation of the maximum value of the sampling period and an interval on the controller gain that guarantees the stabilization of the system.