Mathematical Problems in Engineering 
Volume 2008 (2008), Article ID 270518, 15 pages
doi:10.1155/2008/270518
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

Recommended by Tamas Kalmar-Nagy

Abstract

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.