Lyapunov analysis of nonlinear systems with rational vector field and Jacobian
—This paper studies Lur’e type nonlinear systems where both the vector field and its Jacobian are rational with respect to the states and a sector bounded nonlinearities. Conditions to assess stability and compute induced L2-gain bounds for such systems are cast in terms of rational inequalities. A...
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| Format: | Conference item |
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IEEE
2016
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| _version_ | 1826298204807757824 |
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| author | Drummond, R Valmorbida, G Duncan, S |
| author_facet | Drummond, R Valmorbida, G Duncan, S |
| author_sort | Drummond, R |
| collection | OXFORD |
| description | —This paper studies Lur’e type nonlinear systems where both the vector field and its Jacobian are rational with respect to the states and a sector bounded nonlinearities. Conditions to assess stability and compute induced L2-gain bounds for such systems are cast in terms of rational inequalities. A numerical solution for these inequalities is formulated as a convex optimisation problem given by a sum-of-squares program. Examples are given for nonlinear systems with the arctangent and rational nonlinearities. The proposed method is compared to the Popov and Circle criteria in a numerical example and is shown to outperform both of these classical results. |
| first_indexed | 2024-03-07T04:43:18Z |
| format | Conference item |
| id | oxford-uuid:d262b30f-73af-4e14-8286-6e8e9deab3fe |
| institution | University of Oxford |
| last_indexed | 2024-03-07T04:43:18Z |
| publishDate | 2016 |
| publisher | IEEE |
| record_format | dspace |
| spelling | oxford-uuid:d262b30f-73af-4e14-8286-6e8e9deab3fe2022-03-27T08:03:33ZLyapunov analysis of nonlinear systems with rational vector field and JacobianConference itemhttp://purl.org/coar/resource_type/c_5794uuid:d262b30f-73af-4e14-8286-6e8e9deab3feSymplectic Elements at OxfordIEEE2016Drummond, RValmorbida, GDuncan, S—This paper studies Lur’e type nonlinear systems where both the vector field and its Jacobian are rational with respect to the states and a sector bounded nonlinearities. Conditions to assess stability and compute induced L2-gain bounds for such systems are cast in terms of rational inequalities. A numerical solution for these inequalities is formulated as a convex optimisation problem given by a sum-of-squares program. Examples are given for nonlinear systems with the arctangent and rational nonlinearities. The proposed method is compared to the Popov and Circle criteria in a numerical example and is shown to outperform both of these classical results. |
| spellingShingle | Drummond, R Valmorbida, G Duncan, S Lyapunov analysis of nonlinear systems with rational vector field and Jacobian |
| title | Lyapunov analysis of nonlinear systems with rational vector field and Jacobian |
| title_full | Lyapunov analysis of nonlinear systems with rational vector field and Jacobian |
| title_fullStr | Lyapunov analysis of nonlinear systems with rational vector field and Jacobian |
| title_full_unstemmed | Lyapunov analysis of nonlinear systems with rational vector field and Jacobian |
| title_short | Lyapunov analysis of nonlinear systems with rational vector field and Jacobian |
| title_sort | lyapunov analysis of nonlinear systems with rational vector field and jacobian |
| work_keys_str_mv | AT drummondr lyapunovanalysisofnonlinearsystemswithrationalvectorfieldandjacobian AT valmorbidag lyapunovanalysisofnonlinearsystemswithrationalvectorfieldandjacobian AT duncans lyapunovanalysisofnonlinearsystemswithrationalvectorfieldandjacobian |