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

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 tim...

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Main Authors: Chakib Ben Njima, Walid Ben Mabrouk, Hassani Messaoud, Germain Garcia
Format: Article
Language:English
Published: Wiley 2014-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2014/964143
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author Chakib Ben Njima
Walid Ben Mabrouk
Hassani Messaoud
Germain Garcia
author_facet Chakib Ben Njima
Walid Ben Mabrouk
Hassani Messaoud
Germain Garcia
author_sort Chakib Ben Njima
collection DOAJ
description 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.
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institution OA Journals
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publishDate 2014-01-01
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series Abstract and Applied Analysis
spelling doaj-art-9cfa20fe51904286b8d9795951c3e95f2025-08-20T02:20:18ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/964143964143Finite Time Stabilization of the Four Tanks System: Extensions to the Uncertain SystemsChakib Ben Njima0Walid Ben Mabrouk1Hassani Messaoud2Germain Garcia3Ecole Nationale d’Ingénieurs de Monastir, Université de Monsatir, Rue Ibn El Jazzar, 5019 Monastir, TunisiaEcole Nationale d’Ingénieurs de Monastir, Université de Monsatir, Rue Ibn El Jazzar, 5019 Monastir, TunisiaEcole Nationale d’Ingénieurs de Monastir, Université de Monsatir, Rue Ibn El Jazzar, 5019 Monastir, TunisiaCNRS, LAAS, 7 Avenue du Colonel Roche, 31077 Toulouse, FranceWe 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.http://dx.doi.org/10.1155/2014/964143
spellingShingle Chakib Ben Njima
Walid Ben Mabrouk
Hassani Messaoud
Germain Garcia
Finite Time Stabilization of the Four Tanks System: Extensions to the Uncertain Systems
Abstract and Applied Analysis
title Finite Time Stabilization of the Four Tanks System: Extensions to the Uncertain Systems
title_full Finite Time Stabilization of the Four Tanks System: Extensions to the Uncertain Systems
title_fullStr Finite Time Stabilization of the Four Tanks System: Extensions to the Uncertain Systems
title_full_unstemmed Finite Time Stabilization of the Four Tanks System: Extensions to the Uncertain Systems
title_short Finite Time Stabilization of the Four Tanks System: Extensions to the Uncertain Systems
title_sort finite time stabilization of the four tanks system extensions to the uncertain systems
url http://dx.doi.org/10.1155/2014/964143
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AT walidbenmabrouk finitetimestabilizationofthefourtankssystemextensionstotheuncertainsystems
AT hassanimessaoud finitetimestabilizationofthefourtankssystemextensionstotheuncertainsystems
AT germaingarcia finitetimestabilizationofthefourtankssystemextensionstotheuncertainsystems