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!
|
| Summary: | 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. |
|---|---|
| ISSN: | 1085-3375 1687-0409 |