Forward Euler Solutions and Weakly Invariant Time-Delayed Systems
This paper presents a necessary and sufficient condition for the weak invariance property of a time-delayed system parametrized by a differential inclusion. The aforementioned condition generalizes the well-known Hamilton-Jacobi inequality that characterizes weakly invariant systems in the nondelay...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/481853 |
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| _version_ | 1849435194025574400 |
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| author | Norma L. Ortiz-Robinson Vinicio R. Ríos |
| author_facet | Norma L. Ortiz-Robinson Vinicio R. Ríos |
| author_sort | Norma L. Ortiz-Robinson |
| collection | DOAJ |
| description | This paper presents a necessary and sufficient condition for the weak
invariance property of a time-delayed system parametrized by a differential inclusion.
The aforementioned condition generalizes the well-known Hamilton-Jacobi
inequality that characterizes weakly invariant systems in the nondelay setting. The
forward Euler approximation scheme used in the theory of discontinuous differential
equations is extended to the time-delayed context by incorporating the delay and
tail functions featuring the dynamics. Accordingly, an existence theorem of weakly
invariant trajectories is established under the extended forward Euler approach. |
| format | Article |
| id | doaj-art-de2c03b260404235a7c762966e094f8f |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-de2c03b260404235a7c762966e094f8f2025-08-20T03:26:21ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/481853481853Forward Euler Solutions and Weakly Invariant Time-Delayed SystemsNorma L. Ortiz-Robinson0Vinicio R. Ríos1Department of Mathematics and Applied Mathematics, VA Commonwealth University, Richmond, Virginia 23284, USADepartamento de Matemáticas, Facultad Experimental de Ciencias, Universidad del Zulia, Apartado 526, Maracaibo, Edo Zulia, VenezuelaThis paper presents a necessary and sufficient condition for the weak invariance property of a time-delayed system parametrized by a differential inclusion. The aforementioned condition generalizes the well-known Hamilton-Jacobi inequality that characterizes weakly invariant systems in the nondelay setting. The forward Euler approximation scheme used in the theory of discontinuous differential equations is extended to the time-delayed context by incorporating the delay and tail functions featuring the dynamics. Accordingly, an existence theorem of weakly invariant trajectories is established under the extended forward Euler approach.http://dx.doi.org/10.1155/2012/481853 |
| spellingShingle | Norma L. Ortiz-Robinson Vinicio R. Ríos Forward Euler Solutions and Weakly Invariant Time-Delayed Systems Abstract and Applied Analysis |
| title | Forward Euler Solutions and Weakly Invariant Time-Delayed Systems |
| title_full | Forward Euler Solutions and Weakly Invariant Time-Delayed Systems |
| title_fullStr | Forward Euler Solutions and Weakly Invariant Time-Delayed Systems |
| title_full_unstemmed | Forward Euler Solutions and Weakly Invariant Time-Delayed Systems |
| title_short | Forward Euler Solutions and Weakly Invariant Time-Delayed Systems |
| title_sort | forward euler solutions and weakly invariant time delayed systems |
| url | http://dx.doi.org/10.1155/2012/481853 |
| work_keys_str_mv | AT normalortizrobinson forwardeulersolutionsandweaklyinvarianttimedelayedsystems AT viniciorrios forwardeulersolutionsandweaklyinvarianttimedelayedsystems |