Journal of Applied Mathematics
Volume 2012 (2012), Article ID 684292, 25 pages
Research Article

Stability and Limit Oscillations of a Control Event-Based Sampling Criterion

1Institute for Research and Development of Processes, University of Basque Country, Campus of Leioa (Bizkaia), Apartado 644, Bilbao, Leioa 48090, Spain
2Department of Applied Mathematics, University of Basque Country, Campus of Bilbao (Bizkaia), Apartado 644, Bilbao 48012, Spain
3Department of Telecommunications and Systems Engineering, Autonomous University of Barcelona, Bellaterra 08193, Barcelona, Spain

Received 24 February 2012; Revised 20 April 2012; Accepted 26 April 2012

Academic Editor: Zhiwei Gao

Copyright © 2012 M. De la Sen 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 investigates the presence of limit oscillations in an adaptive sampling system. The basic sampling criterion operates in the sense that each next sampling occurs when the absolute difference of the signal amplitude with respect to its currently sampled signal equalizes a prescribed threshold amplitude. The sampling criterion is extended involving a prescribed set of amplitudes. The limit oscillations might be interpreted through the equivalence of the adaptive sampling and hold device with a nonlinear one consisting of a relay with multiple hysteresis whose parameterization is, in general, dependent on the initial conditions of the dynamic system. The performed study is performed on the time domain.