New Conditions for the Exponential Stability of Nonlinear Differential Equations
We develop a method for proving local exponential stability of nonlinear nonautonomous differential equations as well as pseudo-linear differential systems. The logarithmic norm technique combined with the “freezing” method is used to study stability of differential systems with slowly varying coeff...
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| Format: | Article |
| Language: | English |
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Wiley
2017-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2017/4640835 |
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| _version_ | 1832567582766399488 |
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| author | Rigoberto Medina |
| author_facet | Rigoberto Medina |
| author_sort | Rigoberto Medina |
| collection | DOAJ |
| description | We develop a method for proving local exponential stability of nonlinear nonautonomous differential equations as well as pseudo-linear differential systems. The logarithmic norm technique combined with the “freezing” method is used to study stability of differential systems with slowly varying coefficients and nonlinear perturbations. Testable conditions for local exponential stability of pseudo-linear differential systems are given. Besides, we establish the robustness of the exponential stability in finite-dimensional spaces, in the sense that the exponential stability for a given linear equation persists under sufficiently small perturbations. We illustrate the application of this test to linear approximations of the differential systems under consideration. |
| format | Article |
| id | doaj-art-47dc44eba4bd405fba03bfe109c98954 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2017-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-47dc44eba4bd405fba03bfe109c989542025-02-03T01:01:04ZengWileyAbstract and Applied Analysis1085-33751687-04092017-01-01201710.1155/2017/46408354640835New Conditions for the Exponential Stability of Nonlinear Differential EquationsRigoberto Medina0Departamento de Ciencias Exactas, Universidad de Los Lagos, Casilla 933, Osorno, ChileWe develop a method for proving local exponential stability of nonlinear nonautonomous differential equations as well as pseudo-linear differential systems. The logarithmic norm technique combined with the “freezing” method is used to study stability of differential systems with slowly varying coefficients and nonlinear perturbations. Testable conditions for local exponential stability of pseudo-linear differential systems are given. Besides, we establish the robustness of the exponential stability in finite-dimensional spaces, in the sense that the exponential stability for a given linear equation persists under sufficiently small perturbations. We illustrate the application of this test to linear approximations of the differential systems under consideration.http://dx.doi.org/10.1155/2017/4640835 |
| spellingShingle | Rigoberto Medina New Conditions for the Exponential Stability of Nonlinear Differential Equations Abstract and Applied Analysis |
| title | New Conditions for the Exponential Stability of Nonlinear Differential Equations |
| title_full | New Conditions for the Exponential Stability of Nonlinear Differential Equations |
| title_fullStr | New Conditions for the Exponential Stability of Nonlinear Differential Equations |
| title_full_unstemmed | New Conditions for the Exponential Stability of Nonlinear Differential Equations |
| title_short | New Conditions for the Exponential Stability of Nonlinear Differential Equations |
| title_sort | new conditions for the exponential stability of nonlinear differential equations |
| url | http://dx.doi.org/10.1155/2017/4640835 |
| work_keys_str_mv | AT rigobertomedina newconditionsfortheexponentialstabilityofnonlineardifferentialequations |