About Total Stability of a Class of Nonlinear Dynamic Systems Eventually Subject to Discrete Internal Delays
This paper studies and investigates total stability results of a class of dynamic systems within a prescribed closed ball of the state space around the origin. The class of systems under study includes unstructured nonlinearities subject to multiple higher-order Lipschitz-type conditions which influ...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | International Journal of Differential Equations |
| Online Access: | http://dx.doi.org/10.1155/2021/5593813 |
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| _version_ | 1832558428563701760 |
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| author | Manuel De la Sen |
| author_facet | Manuel De la Sen |
| author_sort | Manuel De la Sen |
| collection | DOAJ |
| description | This paper studies and investigates total stability results of a class of dynamic systems within a prescribed closed ball of the state space around the origin. The class of systems under study includes unstructured nonlinearities subject to multiple higher-order Lipschitz-type conditions which influence the dynamics and which can be eventually interpreted as unstructured perturbations. The results are also extended to the case of presence of multiple internal (i.e., in the state) point discrete delays. Some stability extensions are also discussed for the case when the systems are subject to forcing efforts by using links between the controllability and stabilizability concepts from control theory and the existence of stabilizing linear controls. The results are based on the ad hoc use of Gronwall’s inequality. |
| format | Article |
| id | doaj-art-0697b9d3bc6a4c22abe3ae3ebc1f6ce0 |
| institution | Kabale University |
| issn | 1687-9643 1687-9651 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Differential Equations |
| spelling | doaj-art-0697b9d3bc6a4c22abe3ae3ebc1f6ce02025-02-03T01:32:24ZengWileyInternational Journal of Differential Equations1687-96431687-96512021-01-01202110.1155/2021/55938135593813About Total Stability of a Class of Nonlinear Dynamic Systems Eventually Subject to Discrete Internal DelaysManuel De la Sen0Institute of Research and Development of Processes IIDP, University of the Basque Country, Campus of Leioa, P.O. Box 48940, Leioa, Bizkaia, SpainThis paper studies and investigates total stability results of a class of dynamic systems within a prescribed closed ball of the state space around the origin. The class of systems under study includes unstructured nonlinearities subject to multiple higher-order Lipschitz-type conditions which influence the dynamics and which can be eventually interpreted as unstructured perturbations. The results are also extended to the case of presence of multiple internal (i.e., in the state) point discrete delays. Some stability extensions are also discussed for the case when the systems are subject to forcing efforts by using links between the controllability and stabilizability concepts from control theory and the existence of stabilizing linear controls. The results are based on the ad hoc use of Gronwall’s inequality.http://dx.doi.org/10.1155/2021/5593813 |
| spellingShingle | Manuel De la Sen About Total Stability of a Class of Nonlinear Dynamic Systems Eventually Subject to Discrete Internal Delays International Journal of Differential Equations |
| title | About Total Stability of a Class of Nonlinear Dynamic Systems Eventually Subject to Discrete Internal Delays |
| title_full | About Total Stability of a Class of Nonlinear Dynamic Systems Eventually Subject to Discrete Internal Delays |
| title_fullStr | About Total Stability of a Class of Nonlinear Dynamic Systems Eventually Subject to Discrete Internal Delays |
| title_full_unstemmed | About Total Stability of a Class of Nonlinear Dynamic Systems Eventually Subject to Discrete Internal Delays |
| title_short | About Total Stability of a Class of Nonlinear Dynamic Systems Eventually Subject to Discrete Internal Delays |
| title_sort | about total stability of a class of nonlinear dynamic systems eventually subject to discrete internal delays |
| url | http://dx.doi.org/10.1155/2021/5593813 |
| work_keys_str_mv | AT manueldelasen abouttotalstabilityofaclassofnonlineardynamicsystemseventuallysubjecttodiscreteinternaldelays |