Exponential Stability of Switched Positive Homogeneous Systems
This paper studies the exponential stability of switched positive nonlinear systems defined by cooperative and homogeneous vector fields. In order to capture the decay rate of such systems, we first consider the subsystems. A sufficient condition for exponential stability of subsystems with time-var...
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| Format: | Article |
| Language: | English |
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Wiley
2017-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2017/4326028 |
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| _version_ | 1832554149071290368 |
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| author | Dadong Tian Shutang Liu |
| author_facet | Dadong Tian Shutang Liu |
| author_sort | Dadong Tian |
| collection | DOAJ |
| description | This paper studies the exponential stability of switched positive nonlinear systems defined by cooperative and homogeneous vector fields. In order to capture the decay rate of such systems, we first consider the subsystems. A sufficient condition for exponential stability of subsystems with time-varying delays is derived. In particular, for the corresponding delay-free systems, we prove that this sufficient condition is also necessary. Then, we present a sufficient condition of exponential stability under minimum dwell time switching for the switched positive nonlinear systems. Some results in the previous literature are extended. Finally, a numerical example is given to demonstrate the effectiveness of the obtained results. |
| format | Article |
| id | doaj-art-58dc4fa00a9349d8bf09a527e61fd89f |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2017-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-58dc4fa00a9349d8bf09a527e61fd89f2025-02-03T05:52:16ZengWileyComplexity1076-27871099-05262017-01-01201710.1155/2017/43260284326028Exponential Stability of Switched Positive Homogeneous SystemsDadong Tian0Shutang Liu1College of Control Science and Engineering, Shandong University, Jinan 250061, ChinaCollege of Control Science and Engineering, Shandong University, Jinan 250061, ChinaThis paper studies the exponential stability of switched positive nonlinear systems defined by cooperative and homogeneous vector fields. In order to capture the decay rate of such systems, we first consider the subsystems. A sufficient condition for exponential stability of subsystems with time-varying delays is derived. In particular, for the corresponding delay-free systems, we prove that this sufficient condition is also necessary. Then, we present a sufficient condition of exponential stability under minimum dwell time switching for the switched positive nonlinear systems. Some results in the previous literature are extended. Finally, a numerical example is given to demonstrate the effectiveness of the obtained results.http://dx.doi.org/10.1155/2017/4326028 |
| spellingShingle | Dadong Tian Shutang Liu Exponential Stability of Switched Positive Homogeneous Systems Complexity |
| title | Exponential Stability of Switched Positive Homogeneous Systems |
| title_full | Exponential Stability of Switched Positive Homogeneous Systems |
| title_fullStr | Exponential Stability of Switched Positive Homogeneous Systems |
| title_full_unstemmed | Exponential Stability of Switched Positive Homogeneous Systems |
| title_short | Exponential Stability of Switched Positive Homogeneous Systems |
| title_sort | exponential stability of switched positive homogeneous systems |
| url | http://dx.doi.org/10.1155/2017/4326028 |
| work_keys_str_mv | AT dadongtian exponentialstabilityofswitchedpositivehomogeneoussystems AT shutangliu exponentialstabilityofswitchedpositivehomogeneoussystems |