Solutions to Lyapunov stability problems: nonlinear systems with continuous motions
The necessary and sufficient conditions for accurate construction of a Lyapunov function and the necessary and sufficient conditions for a set to be the asymptotic stability domain are algorithmically solved for a nonlinear dynamical system with continuous motions. The conditions are established by...
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| Format: | Article |
| Language: | English |
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Wiley
1994-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171294000839 |
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| _version_ | 1832564313525583872 |
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| author | Ljubomir T. Grujic |
| author_facet | Ljubomir T. Grujic |
| author_sort | Ljubomir T. Grujic |
| collection | DOAJ |
| description | The necessary and sufficient conditions for accurate construction of a Lyapunov function and the necessary and sufficient conditions for a set to be the asymptotic stability domain are algorithmically solved for a nonlinear dynamical system with continuous motions. The conditions are established by utilizing properties of o-uniquely bounded sets, which are explained in the paper. They allow arbitrary selection of an o-uniquely bounded set to generate a Lyapunov function. |
| format | Article |
| id | doaj-art-1c652b6a106c4122ab1b0f038e0fd1ad |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1994-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-1c652b6a106c4122ab1b0f038e0fd1ad2025-02-03T01:11:12ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251994-01-0117358759610.1155/S0161171294000839Solutions to Lyapunov stability problems: nonlinear systems with continuous motionsLjubomir T. Grujic0Faculty of Mechanical Engineering, University in Belgrade, P.O. Box 174, Belgrade 11000, SerbiaThe necessary and sufficient conditions for accurate construction of a Lyapunov function and the necessary and sufficient conditions for a set to be the asymptotic stability domain are algorithmically solved for a nonlinear dynamical system with continuous motions. The conditions are established by utilizing properties of o-uniquely bounded sets, which are explained in the paper. They allow arbitrary selection of an o-uniquely bounded set to generate a Lyapunov function.http://dx.doi.org/10.1155/S0161171294000839stabilityLyapunov methodLyapunov functionsnonlinear systemsdynamical systems. |
| spellingShingle | Ljubomir T. Grujic Solutions to Lyapunov stability problems: nonlinear systems with continuous motions International Journal of Mathematics and Mathematical Sciences stability Lyapunov method Lyapunov functions nonlinear systems dynamical systems. |
| title | Solutions to Lyapunov stability problems: nonlinear systems with continuous motions |
| title_full | Solutions to Lyapunov stability problems: nonlinear systems with continuous motions |
| title_fullStr | Solutions to Lyapunov stability problems: nonlinear systems with continuous motions |
| title_full_unstemmed | Solutions to Lyapunov stability problems: nonlinear systems with continuous motions |
| title_short | Solutions to Lyapunov stability problems: nonlinear systems with continuous motions |
| title_sort | solutions to lyapunov stability problems nonlinear systems with continuous motions |
| topic | stability Lyapunov method Lyapunov functions nonlinear systems dynamical systems. |
| url | http://dx.doi.org/10.1155/S0161171294000839 |
| work_keys_str_mv | AT ljubomirtgrujic solutionstolyapunovstabilityproblemsnonlinearsystemswithcontinuousmotions |