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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 964143, 7 pages
http://dx.doi.org/10.1155/2014/964143
Research Article

Finite Time Stabilization of the Four Tanks System: Extensions to the Uncertain Systems

1Ecole Nationale d’Ingénieurs de Monastir, Université de Monsatir, Rue Ibn El Jazzar, 5019 Monastir, Tunisia
2CNRS, LAAS, 7 Avenue du Colonel Roche, 31077 Toulouse, France
3Université de Toulouse, UPS, INSA, INP, ISAE, LAAS, 7 Avenue du Colonel Roche, F-31077 Toulouse, France

Received 26 November 2013; Accepted 13 January 2014; Published 4 March 2014

Academic Editor: Hui Zhang

Copyright © 2014 Chakib Ben Njima 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.

Abstract

We consider the finite time stability and stabilization of linear systems described in continuous time. First, we provide a condition for the stability over time using the state transition matrix standard. Then we give conditions to design a state feedback control that stabilizes the system over time. In some cases where there is uncertainty in the system model, the previous conditions are extended to a certain class of uncertain systems. The considered uncertainties are the polytopic and norm bounded ones. To reveal the proposed approach, an application to the four tanks system was made.