Relative Nonlinear Measure Method to Exponential Stability of Impulsive Delayed Differential Equations
This paper is devoted to providing a novel method to global exponential stability of impulsive delayed differential equations. By utilizing relative nonlinear measure method, several global exponential stability criteria are presented for the impulsive delayed differential equations. Compared with t...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/760893 |
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| _version_ | 1832551465130917888 |
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| author | Xueli Song Xing Xin Huiya Dai Jigen Peng |
| author_facet | Xueli Song Xing Xin Huiya Dai Jigen Peng |
| author_sort | Xueli Song |
| collection | DOAJ |
| description | This paper is devoted to providing a novel method to global exponential stability of impulsive delayed differential equations. By utilizing relative nonlinear measure method, several global exponential stability criteria are presented for the impulsive delayed differential equations. Compared with the Razumikhin technique and Lyapunov function method, our method is less conservative and gives a convergence rate, and one of our stability criteria is more flexible by incorporating an adjustable matrix. An example and its simulation are provided to illustrate that our method is efficient and our results are new and correct. |
| format | Article |
| id | doaj-art-62d08e87e1fe4d90aadf5e625e898d03 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-62d08e87e1fe4d90aadf5e625e898d032025-02-03T06:01:28ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/760893760893Relative Nonlinear Measure Method to Exponential Stability of Impulsive Delayed Differential EquationsXueli Song0Xing Xin1Huiya Dai2Jigen Peng3Department of Mathematics and Information Science, Chang’an University, Xi’an 710064, ChinaThe 41st Institute of the Fourth Academy of CASC, Xi’an 710025, ChinaSchool of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an 710049, ChinaSchool of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an 710049, ChinaThis paper is devoted to providing a novel method to global exponential stability of impulsive delayed differential equations. By utilizing relative nonlinear measure method, several global exponential stability criteria are presented for the impulsive delayed differential equations. Compared with the Razumikhin technique and Lyapunov function method, our method is less conservative and gives a convergence rate, and one of our stability criteria is more flexible by incorporating an adjustable matrix. An example and its simulation are provided to illustrate that our method is efficient and our results are new and correct.http://dx.doi.org/10.1155/2013/760893 |
| spellingShingle | Xueli Song Xing Xin Huiya Dai Jigen Peng Relative Nonlinear Measure Method to Exponential Stability of Impulsive Delayed Differential Equations Abstract and Applied Analysis |
| title | Relative Nonlinear Measure Method to Exponential Stability of Impulsive Delayed Differential Equations |
| title_full | Relative Nonlinear Measure Method to Exponential Stability of Impulsive Delayed Differential Equations |
| title_fullStr | Relative Nonlinear Measure Method to Exponential Stability of Impulsive Delayed Differential Equations |
| title_full_unstemmed | Relative Nonlinear Measure Method to Exponential Stability of Impulsive Delayed Differential Equations |
| title_short | Relative Nonlinear Measure Method to Exponential Stability of Impulsive Delayed Differential Equations |
| title_sort | relative nonlinear measure method to exponential stability of impulsive delayed differential equations |
| url | http://dx.doi.org/10.1155/2013/760893 |
| work_keys_str_mv | AT xuelisong relativenonlinearmeasuremethodtoexponentialstabilityofimpulsivedelayeddifferentialequations AT xingxin relativenonlinearmeasuremethodtoexponentialstabilityofimpulsivedelayeddifferentialequations AT huiyadai relativenonlinearmeasuremethodtoexponentialstabilityofimpulsivedelayeddifferentialequations AT jigenpeng relativenonlinearmeasuremethodtoexponentialstabilityofimpulsivedelayeddifferentialequations |