Mathematical Problems in Engineering
Volume 2011 (2011), Article ID 120570, 16 pages
Research Article

Digital Repetitive Control under Nonuniform Sampling: An LMI Stability Analysis

1Department of Electrical and Electronic Engineering, Universidad Nacional de Colombia, 111321 Bogotá DC, Colombia
2Department of Applied Mathematics IV, Universitat Politècnica de Catalunya, 08800 Vilanova i la Geltrú, Spain
3Institute of Industrial and Control Engineering, Universitat Politècnica de Catalunya, 08028 Barcelona, Spain

Received 9 December 2010; Accepted 10 June 2011

Academic Editor: Dane Quinn

Copyright © 2011 Germán A. Ramos 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.


Digital repetitive control is a technique which allows tracking periodic references and/or rejecting periodic disturbances. Repetitive controllers are usually designed assuming a fixed fundamental frequency for the signals to be tracked/rejected and its main drawback being a dramatic performance decay when this frequency varies. A usual approach to overcome the problem consists of an adaptive change of the sampling period according to the reference/disturbance period variation. This paper presents a stability analysis of a digital repetitive controller working under time-varying sampling period by means of an LMI gridding approach. Theoretical developments are illustrated with experimental results, which are preceded by a detailed description of fundamental issues related to the implementation procedure.