An LMI Approach to Stability for Linear Time-Varying System with Nonlinear Perturbation on Time Scales
We consider Lyapunov stability theory of linear time-varying system and derive sufficient conditions for uniform stability, uniform exponential stability, 𝜓-uniform stability, and h-stability for linear time-varying system with nonlinear perturbation on time scales. We construct appropriate Lyapunov...
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| Format: | Article |
| Language: | English |
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Wiley
2011-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2011/860506 |
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| _version_ | 1832545822030430208 |
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| author | Kanit Mukdasai Piyapong Niamsup |
| author_facet | Kanit Mukdasai Piyapong Niamsup |
| author_sort | Kanit Mukdasai |
| collection | DOAJ |
| description | We consider Lyapunov stability theory of linear time-varying system and derive sufficient conditions for uniform stability, uniform exponential stability, 𝜓-uniform stability, and h-stability for linear time-varying system with nonlinear perturbation on time scales. We construct appropriate Lyapunov functions and derive several stability conditions. Numerical examples are presented to illustrate the effectiveness of the theoretical results. |
| format | Article |
| id | doaj-art-ed5fcb21f1bb4302b8f021acf463685a |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-ed5fcb21f1bb4302b8f021acf463685a2025-02-03T07:24:42ZengWileyAbstract and Applied Analysis1085-33751687-04092011-01-01201110.1155/2011/860506860506An LMI Approach to Stability for Linear Time-Varying System with Nonlinear Perturbation on Time ScalesKanit Mukdasai0Piyapong Niamsup1Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, ThailandDepartment of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai, 50200, ThailandWe consider Lyapunov stability theory of linear time-varying system and derive sufficient conditions for uniform stability, uniform exponential stability, 𝜓-uniform stability, and h-stability for linear time-varying system with nonlinear perturbation on time scales. We construct appropriate Lyapunov functions and derive several stability conditions. Numerical examples are presented to illustrate the effectiveness of the theoretical results.http://dx.doi.org/10.1155/2011/860506 |
| spellingShingle | Kanit Mukdasai Piyapong Niamsup An LMI Approach to Stability for Linear Time-Varying System with Nonlinear Perturbation on Time Scales Abstract and Applied Analysis |
| title | An LMI Approach to Stability for Linear Time-Varying System with Nonlinear Perturbation on Time Scales |
| title_full | An LMI Approach to Stability for Linear Time-Varying System with Nonlinear Perturbation on Time Scales |
| title_fullStr | An LMI Approach to Stability for Linear Time-Varying System with Nonlinear Perturbation on Time Scales |
| title_full_unstemmed | An LMI Approach to Stability for Linear Time-Varying System with Nonlinear Perturbation on Time Scales |
| title_short | An LMI Approach to Stability for Linear Time-Varying System with Nonlinear Perturbation on Time Scales |
| title_sort | lmi approach to stability for linear time varying system with nonlinear perturbation on time scales |
| url | http://dx.doi.org/10.1155/2011/860506 |
| work_keys_str_mv | AT kanitmukdasai anlmiapproachtostabilityforlineartimevaryingsystemwithnonlinearperturbationontimescales AT piyapongniamsup anlmiapproachtostabilityforlineartimevaryingsystemwithnonlinearperturbationontimescales AT kanitmukdasai lmiapproachtostabilityforlineartimevaryingsystemwithnonlinearperturbationontimescales AT piyapongniamsup lmiapproachtostabilityforlineartimevaryingsystemwithnonlinearperturbationontimescales |