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Abstract and Applied Analysis
Volume 2013, Article ID 382762, 14 pages
Research Article

Asymptotic Hyperstability of a Class of Linear Systems under Impulsive Controls Subject to an Integral Popovian Constraint

1Department of Electricity and Electronics, Institute of Research and Development of Processes, University of Basque Country, Campus of Leioa (Bizkaia), Apartado 644, 48940 Bilbao, Spain
2Department of Telecommunications and Systems Engineering, Universitat Autònoma de Barcelona (UAB), 08193 Barcelona, Spain

Received 24 May 2013; Accepted 6 August 2013

Academic Editor: Hamid Reza Karimi

Copyright © 2013 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 is focused on the study of the important property of the asymptotic hyperstability of a class of continuous-time dynamic systems. The presence of a parallel connection of a strictly stable subsystem to an asymptotically hyperstable one in the feed-forward loop is allowed while it has also admitted the generation of a finite or infinite number of impulsive control actions which can be combined with a general form of nonimpulsive controls. The asymptotic hyperstability property is guaranteed under a set of sufficiency-type conditions for the impulsive controls.