A Generalized Nonuniform Contraction and Lyapunov Function
For nonautonomous linear equations x′=A(t)x, we give a complete characterization of general nonuniform contractions in terms of Lyapunov functions. We consider the general case of nonuniform contractions, which corresponds to the existence of what we call nonuniform (D,μ)-contractions. As an applic...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2012-01-01
|
| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/613038 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832548116923940864 |
|---|---|
| author | Fang-fang Liao Yongxin Jiang Zhiting Xie |
| author_facet | Fang-fang Liao Yongxin Jiang Zhiting Xie |
| author_sort | Fang-fang Liao |
| collection | DOAJ |
| description | For nonautonomous linear equations x′=A(t)x, we give a complete
characterization of general nonuniform contractions in terms of Lyapunov
functions. We consider the general case of nonuniform contractions, which
corresponds to the existence of what we call nonuniform (D,μ)-contractions.
As an application, we establish the robustness of the nonuniform contraction under sufficiently small linear perturbations. Moreover, we show that the stability of a nonuniform contraction persists under sufficiently small nonlinear perturbations. |
| format | Article |
| id | doaj-art-556d6ca31787493eb70a3559df4e1e12 |
| 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-556d6ca31787493eb70a3559df4e1e122025-02-03T06:42:11ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/613038613038A Generalized Nonuniform Contraction and Lyapunov FunctionFang-fang Liao0Yongxin Jiang1Zhiting Xie2Nanjing College of Information Technology, Nanjing 210046, ChinaDepartment of Mathematics, College of Science, Hohai University, Nanjing 210098, ChinaDepartment of Mathematics, College of Science, Hohai University, Nanjing 210098, ChinaFor nonautonomous linear equations x′=A(t)x, we give a complete characterization of general nonuniform contractions in terms of Lyapunov functions. We consider the general case of nonuniform contractions, which corresponds to the existence of what we call nonuniform (D,μ)-contractions. As an application, we establish the robustness of the nonuniform contraction under sufficiently small linear perturbations. Moreover, we show that the stability of a nonuniform contraction persists under sufficiently small nonlinear perturbations.http://dx.doi.org/10.1155/2012/613038 |
| spellingShingle | Fang-fang Liao Yongxin Jiang Zhiting Xie A Generalized Nonuniform Contraction and Lyapunov Function Abstract and Applied Analysis |
| title | A Generalized Nonuniform Contraction and Lyapunov Function |
| title_full | A Generalized Nonuniform Contraction and Lyapunov Function |
| title_fullStr | A Generalized Nonuniform Contraction and Lyapunov Function |
| title_full_unstemmed | A Generalized Nonuniform Contraction and Lyapunov Function |
| title_short | A Generalized Nonuniform Contraction and Lyapunov Function |
| title_sort | generalized nonuniform contraction and lyapunov function |
| url | http://dx.doi.org/10.1155/2012/613038 |
| work_keys_str_mv | AT fangfangliao ageneralizednonuniformcontractionandlyapunovfunction AT yongxinjiang ageneralizednonuniformcontractionandlyapunovfunction AT zhitingxie ageneralizednonuniformcontractionandlyapunovfunction AT fangfangliao generalizednonuniformcontractionandlyapunovfunction AT yongxinjiang generalizednonuniformcontractionandlyapunovfunction AT zhitingxie generalizednonuniformcontractionandlyapunovfunction |