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Abstract and Applied Analysis
Volume 2012, Article ID 808290, 16 pages
Research Article

Well-Posedness of Reset Control Systems as State-Dependent Impulsive Dynamical Systems

1Departamento de Informática y Sistemas, Universidad DE Murcia, 30071 Murcia, Spain
2Departamento de Ingenieria Sistemas y Automatica, Universidad Politécnica de Cartagena, Cartagena, Spain

Received 23 April 2012; Accepted 27 September 2012

Academic Editor: Elena Braverman

Copyright © 2012 Alfonso Baños and Juan I. Mulero. 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.


Reset control systems are a special type of state-dependent impulsive dynamic systems, in which the time evolution depends both on continuous dynamics between resets and the discrete dynamics corresponding to the resetting times. This work is devoted to investigate well-posedness of reset control systems, taking as starting point the classical definition of Clegg and Horowitz. Well-posedness is related to the existence and uniqueness of solutions, and in particular to the resetting times to be well defined and distinct. A sufficient condition is developed for a reset system to have well-posed resetting times, which is also a sufficient condition for avoiding Zeno solutions and, thus, for a reset control system to be well-posed.