Exact Asymptotic Stability Analysis and Region-of-Attraction Estimation for Nonlinear Systems
We address the problem of asymptotic stability and region-of-attraction analysis of nonlinear dynamical systems. A hybrid symbolic-numeric method is presented to compute exact Lyapunov functions and exact estimates of regions of attraction of nonlinear systems efficiently. A numerical Lyapunov funct...
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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/10.1155/2013/146137 |
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| _version_ | 1832549505157824512 |
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| author | Min Wu Zhengfeng Yang Wang Lin |
| author_facet | Min Wu Zhengfeng Yang Wang Lin |
| author_sort | Min Wu |
| collection | DOAJ |
| description | We address the problem of asymptotic stability and region-of-attraction analysis of nonlinear dynamical systems. A hybrid symbolic-numeric method is presented to compute exact Lyapunov functions and exact estimates of regions of attraction of nonlinear systems efficiently. A numerical Lyapunov function and an estimate of region of attraction can be obtained by solving an (bilinear) SOS programming via BMI solver, then the modified Newton refinement and rational vector recovery techniques are applied to obtain exact Lyapunov functions and verified estimates of regions of attraction with rational coefficients. Experiments on some benchmarks are given to illustrate the efficiency of our algorithm. |
| format | Article |
| id | doaj-art-4a414ee8c0c746fe8cf435cecb02b431 |
| 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-4a414ee8c0c746fe8cf435cecb02b4312025-02-03T06:11:05ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/146137146137Exact Asymptotic Stability Analysis and Region-of-Attraction Estimation for Nonlinear SystemsMin Wu0Zhengfeng Yang1Wang Lin2Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai 200062, ChinaShanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai 200062, ChinaCollege of Mathematics and Information Science, Wenzhou University, Wenzhou Zhejiang 325035, ChinaWe address the problem of asymptotic stability and region-of-attraction analysis of nonlinear dynamical systems. A hybrid symbolic-numeric method is presented to compute exact Lyapunov functions and exact estimates of regions of attraction of nonlinear systems efficiently. A numerical Lyapunov function and an estimate of region of attraction can be obtained by solving an (bilinear) SOS programming via BMI solver, then the modified Newton refinement and rational vector recovery techniques are applied to obtain exact Lyapunov functions and verified estimates of regions of attraction with rational coefficients. Experiments on some benchmarks are given to illustrate the efficiency of our algorithm.http://dx.doi.org/10.1155/2013/146137 |
| spellingShingle | Min Wu Zhengfeng Yang Wang Lin Exact Asymptotic Stability Analysis and Region-of-Attraction Estimation for Nonlinear Systems Abstract and Applied Analysis |
| title | Exact Asymptotic Stability Analysis and Region-of-Attraction Estimation for Nonlinear Systems |
| title_full | Exact Asymptotic Stability Analysis and Region-of-Attraction Estimation for Nonlinear Systems |
| title_fullStr | Exact Asymptotic Stability Analysis and Region-of-Attraction Estimation for Nonlinear Systems |
| title_full_unstemmed | Exact Asymptotic Stability Analysis and Region-of-Attraction Estimation for Nonlinear Systems |
| title_short | Exact Asymptotic Stability Analysis and Region-of-Attraction Estimation for Nonlinear Systems |
| title_sort | exact asymptotic stability analysis and region of attraction estimation for nonlinear systems |
| url | http://dx.doi.org/10.1155/2013/146137 |
| work_keys_str_mv | AT minwu exactasymptoticstabilityanalysisandregionofattractionestimationfornonlinearsystems AT zhengfengyang exactasymptoticstabilityanalysisandregionofattractionestimationfornonlinearsystems AT wanglin exactasymptoticstabilityanalysisandregionofattractionestimationfornonlinearsystems |