Linearization of impulsive differential equations with ordinary dichotomy
This paper presents a linearization theorem for the impulsive differential equations when the linear system has ordinary dichotomy. We prove that when the linear impulsive system has ordinary dichotomy, the nonlinear system x ̇(t)=A(t)x(t)+f(t,x), t≠t_k, ∆x(t_k )= A ̃(t_k )x(t_k )+ f ̃(t_k,x), k∈Z i...
| Main Authors: | , , , |
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| Other Authors: | |
| Format: | Journal Article |
| Language: | English |
| Published: |
2014
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| Subjects: | |
| Online Access: | https://hdl.handle.net/10356/104846 http://hdl.handle.net/10220/20366 |
| _version_ | 1811678847912902656 |
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| author | Wong, P. J. Y. Gao, Yongfei Yuan, Xiaoqing Xia, Yonghui |
| author2 | School of Electrical and Electronic Engineering |
| author_facet | School of Electrical and Electronic Engineering Wong, P. J. Y. Gao, Yongfei Yuan, Xiaoqing Xia, Yonghui |
| author_sort | Wong, P. J. Y. |
| collection | NTU |
| description | This paper presents a linearization theorem for the impulsive differential equations when the linear system has ordinary dichotomy. We prove that when the linear impulsive system has ordinary dichotomy, the nonlinear system x ̇(t)=A(t)x(t)+f(t,x), t≠t_k, ∆x(t_k )= A ̃(t_k )x(t_k )+ f ̃(t_k,x), k∈Z is topologically conjugated to x ̇(t)=A(t)x(t), t≠t_k, ∆x(t_k )= A ̃(t_k )x(t_k ), k∈Z, where ∆x(t_k )=x(t_k^+ )-x(t_k^-), x(t_k^- )= x(t_k), represents the jump of the solution x(t) at t= t_k. Finally, two examples are given to show the feasibility of our results. |
| first_indexed | 2024-10-01T02:59:46Z |
| format | Journal Article |
| id | ntu-10356/104846 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T02:59:46Z |
| publishDate | 2014 |
| record_format | dspace |
| spelling | ntu-10356/1048462020-03-07T14:00:36Z Linearization of impulsive differential equations with ordinary dichotomy Wong, P. J. Y. Gao, Yongfei Yuan, Xiaoqing Xia, Yonghui School of Electrical and Electronic Engineering DRNTU::Engineering::Electrical and electronic engineering This paper presents a linearization theorem for the impulsive differential equations when the linear system has ordinary dichotomy. We prove that when the linear impulsive system has ordinary dichotomy, the nonlinear system x ̇(t)=A(t)x(t)+f(t,x), t≠t_k, ∆x(t_k )= A ̃(t_k )x(t_k )+ f ̃(t_k,x), k∈Z is topologically conjugated to x ̇(t)=A(t)x(t), t≠t_k, ∆x(t_k )= A ̃(t_k )x(t_k ), k∈Z, where ∆x(t_k )=x(t_k^+ )-x(t_k^-), x(t_k^- )= x(t_k), represents the jump of the solution x(t) at t= t_k. Finally, two examples are given to show the feasibility of our results. Published version 2014-08-21T06:15:39Z 2019-12-06T21:41:05Z 2014-08-21T06:15:39Z 2019-12-06T21:41:05Z 2014 2014 Journal Article Gao, Y., Yuan, X., Xia, Y., & Wong, P. J. Y. (2014). Linearization of Impulsive Differential Equations with Ordinary Dichotomy. Abstract and Applied Analysis, 2014, 632109-. 1085-3375 https://hdl.handle.net/10356/104846 http://hdl.handle.net/10220/20366 10.1155/2014/632109 en Abstract and applied analysis Copyright © 2014 Yongfei Gao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. application/pdf |
| spellingShingle | DRNTU::Engineering::Electrical and electronic engineering Wong, P. J. Y. Gao, Yongfei Yuan, Xiaoqing Xia, Yonghui Linearization of impulsive differential equations with ordinary dichotomy |
| title | Linearization of impulsive differential equations with ordinary dichotomy |
| title_full | Linearization of impulsive differential equations with ordinary dichotomy |
| title_fullStr | Linearization of impulsive differential equations with ordinary dichotomy |
| title_full_unstemmed | Linearization of impulsive differential equations with ordinary dichotomy |
| title_short | Linearization of impulsive differential equations with ordinary dichotomy |
| title_sort | linearization of impulsive differential equations with ordinary dichotomy |
| topic | DRNTU::Engineering::Electrical and electronic engineering |
| url | https://hdl.handle.net/10356/104846 http://hdl.handle.net/10220/20366 |
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