Initial Time Difference Stability of Causal Differential Systems in terms of Lyapunov Functions and Lyapunov Functionals
We investigate the qualitative behavior of a perturbed causal differential equation that differs in initial position and initial time with respect to the unperturbed causal differential equations. We compare the classical notion of stability of the causal differential systems to the notion of initi...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2014/832015 |
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| _version_ | 1841524634354188288 |
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| author | Coşkun Yakar Mustafa Bayram Gücen |
| author_facet | Coşkun Yakar Mustafa Bayram Gücen |
| author_sort | Coşkun Yakar |
| collection | DOAJ |
| description | We investigate the qualitative behavior of a perturbed causal differential equation that differs in initial position and initial time with respect to the unperturbed causal differential equations.
We compare the classical notion of stability of the causal differential systems to the notion of initial time difference stability of causal differential systems and present a comparison result in terms of Lyapunov functions. We have utilized Lyapunov functions and Lyapunov functional in the study of stability theory of causal differential systems when establishing initial time difference stability of the perturbed causal differential system with respect to the unperturbed causal differential system. |
| format | Article |
| id | doaj-art-72b64c6751ad4ca6a48f4e97e43195d6 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-72b64c6751ad4ca6a48f4e97e43195d62025-02-03T05:47:44ZengWileyJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/832015832015Initial Time Difference Stability of Causal Differential Systems in terms of Lyapunov Functions and Lyapunov FunctionalsCoşkun Yakar0Mustafa Bayram Gücen1Department of Mathematics, Gebze Technical University, Gebze, 141-41400 Kocaeli, TurkeyDepartment of Mathematics, Faculty of Sciences, Yıldız Technical University, Istanbul, TurkeyWe investigate the qualitative behavior of a perturbed causal differential equation that differs in initial position and initial time with respect to the unperturbed causal differential equations. We compare the classical notion of stability of the causal differential systems to the notion of initial time difference stability of causal differential systems and present a comparison result in terms of Lyapunov functions. We have utilized Lyapunov functions and Lyapunov functional in the study of stability theory of causal differential systems when establishing initial time difference stability of the perturbed causal differential system with respect to the unperturbed causal differential system.http://dx.doi.org/10.1155/2014/832015 |
| spellingShingle | Coşkun Yakar Mustafa Bayram Gücen Initial Time Difference Stability of Causal Differential Systems in terms of Lyapunov Functions and Lyapunov Functionals Journal of Applied Mathematics |
| title | Initial Time Difference Stability of Causal Differential Systems in terms of Lyapunov Functions and Lyapunov Functionals |
| title_full | Initial Time Difference Stability of Causal Differential Systems in terms of Lyapunov Functions and Lyapunov Functionals |
| title_fullStr | Initial Time Difference Stability of Causal Differential Systems in terms of Lyapunov Functions and Lyapunov Functionals |
| title_full_unstemmed | Initial Time Difference Stability of Causal Differential Systems in terms of Lyapunov Functions and Lyapunov Functionals |
| title_short | Initial Time Difference Stability of Causal Differential Systems in terms of Lyapunov Functions and Lyapunov Functionals |
| title_sort | initial time difference stability of causal differential systems in terms of lyapunov functions and lyapunov functionals |
| url | http://dx.doi.org/10.1155/2014/832015 |
| work_keys_str_mv | AT coskunyakar initialtimedifferencestabilityofcausaldifferentialsystemsintermsoflyapunovfunctionsandlyapunovfunctionals AT mustafabayramgucen initialtimedifferencestabilityofcausaldifferentialsystemsintermsoflyapunovfunctionsandlyapunovfunctionals |