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: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/964143 |
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| _version_ | 1850171351994728448 |
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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. |
| format | Article |
| id | doaj-art-9cfa20fe51904286b8d9795951c3e95f |
| institution | OA Journals |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| 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 |
| work_keys_str_mv | AT chakibbennjima finitetimestabilizationofthefourtankssystemextensionstotheuncertainsystems AT walidbenmabrouk finitetimestabilizationofthefourtankssystemextensionstotheuncertainsystems AT hassanimessaoud finitetimestabilizationofthefourtankssystemextensionstotheuncertainsystems AT germaingarcia finitetimestabilizationofthefourtankssystemextensionstotheuncertainsystems |