Controllability and feedback stabilizability in a nonuniform framework
We propose a new controllability property for linear nonautonomous control systems in finite dimension: the nonuniform complete controllability, which is halfway between the classical Kalman’s properties of complete controllability and uniform complete controllability. This new concept has a strong...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Académie des sciences
2024-11-01
|
| Series: | Comptes Rendus. Mathématique |
| Subjects: | |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.672/ |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1825206143577751552 |
|---|---|
| author | Huerta, Ignacio Monzón, Pablo Robledo, Gonzalo |
| author_facet | Huerta, Ignacio Monzón, Pablo Robledo, Gonzalo |
| author_sort | Huerta, Ignacio |
| collection | DOAJ |
| description | We propose a new controllability property for linear nonautonomous control systems in finite dimension: the nonuniform complete controllability, which is halfway between the classical Kalman’s properties of complete controllability and uniform complete controllability. This new concept has a strong linkage, as we prove, with the property of nonuniform bounded growth for the corresponding plant. In addition, we also prove that if a control system is nonuniformly completely controllable and its plant (uncontrolled part) has the property of nonuniform bounded growth, then there exist a linear feedback control leading to a nonuniformly exponentially stable closed–loop system. |
| format | Article |
| id | doaj-art-3ae72d8e0f1d4162b03c8de1525c6103 |
| institution | Kabale University |
| issn | 1778-3569 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj-art-3ae72d8e0f1d4162b03c8de1525c61032025-02-07T11:26:37ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692024-11-01362G121667169210.5802/crmath.67210.5802/crmath.672Controllability and feedback stabilizability in a nonuniform frameworkHuerta, Ignacio0Monzón, Pablo1Robledo, Gonzalo2Departamento de Matemática, Universidad Técnica Federico Santa María, Casilla 110-V, Valparaíso, ChileFacultad de Ingeniería – Universidad de la República, Julio Herrera y Reissig 565, Montevideo, UruguayDepartamento de Matemáticas – Universidad de Chile, Casilla 653, Las Palmeras 3425, Ñuñoa – Santiago, ChileWe propose a new controllability property for linear nonautonomous control systems in finite dimension: the nonuniform complete controllability, which is halfway between the classical Kalman’s properties of complete controllability and uniform complete controllability. This new concept has a strong linkage, as we prove, with the property of nonuniform bounded growth for the corresponding plant. In addition, we also prove that if a control system is nonuniformly completely controllable and its plant (uncontrolled part) has the property of nonuniform bounded growth, then there exist a linear feedback control leading to a nonuniformly exponentially stable closed–loop system.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.672/Linear nonautonomous systemsnonuniform controllabilitynonuniform exponential stabilizabilitynonuniform bounded growth |
| spellingShingle | Huerta, Ignacio Monzón, Pablo Robledo, Gonzalo Controllability and feedback stabilizability in a nonuniform framework Comptes Rendus. Mathématique Linear nonautonomous systems nonuniform controllability nonuniform exponential stabilizability nonuniform bounded growth |
| title | Controllability and feedback stabilizability in a nonuniform framework |
| title_full | Controllability and feedback stabilizability in a nonuniform framework |
| title_fullStr | Controllability and feedback stabilizability in a nonuniform framework |
| title_full_unstemmed | Controllability and feedback stabilizability in a nonuniform framework |
| title_short | Controllability and feedback stabilizability in a nonuniform framework |
| title_sort | controllability and feedback stabilizability in a nonuniform framework |
| topic | Linear nonautonomous systems nonuniform controllability nonuniform exponential stabilizability nonuniform bounded growth |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.672/ |
| work_keys_str_mv | AT huertaignacio controllabilityandfeedbackstabilizabilityinanonuniformframework AT monzonpablo controllabilityandfeedbackstabilizabilityinanonuniformframework AT robledogonzalo controllabilityandfeedbackstabilizabilityinanonuniformframework |