On the Passivity and Positivity Properties in Dynamic Systems: Their Achievement under Control Laws and Their Maintenance under Parameterizations Switching
This paper is devoted to discuss certain aspects of passivity results in dynamic systems and the characterization of the regenerative systems counterparts. In particular, the various concepts of passivity as standard passivity, strict input passivity, strict output passivity, and very strict passivi...
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| Format: | Article |
| Language: | English |
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Wiley
2018-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2018/5298756 |
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| _version_ | 1849306978512273408 |
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| author | M. De la Sen |
| author_facet | M. De la Sen |
| author_sort | M. De la Sen |
| collection | DOAJ |
| description | This paper is devoted to discuss certain aspects of passivity results in dynamic systems and the characterization of the regenerative systems counterparts. In particular, the various concepts of passivity as standard passivity, strict input passivity, strict output passivity, and very strict passivity (i.e., joint strict input and output passivity) are given and related to the existence of a storage function and a dissipation function. Later on, the obtained results are related to external positivity of systems and positivity or strict positivity of the transfer matrices and transfer functions in the time-invariant case. On the other hand, how to achieve or how eventually to increase the passivity effects via linear feedback by the synthesis of the appropriate feed-forward or feedback controllers or, simply, by adding a positive parallel direct input-output matrix interconnection gain is discussed. |
| format | Article |
| id | doaj-art-2488c8e54c6f4249ba97bcb4b47268f5 |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-2488c8e54c6f4249ba97bcb4b47268f52025-08-20T03:54:53ZengWileyJournal of Mathematics2314-46292314-47852018-01-01201810.1155/2018/52987565298756On the Passivity and Positivity Properties in Dynamic Systems: Their Achievement under Control Laws and Their Maintenance under Parameterizations SwitchingM. De la Sen0Institute of Research and Development of Processes (IIDP), University of the Basque Country, Campus of Leioa, P.O. Box 48940, Leioa, Bizkaia, SpainThis paper is devoted to discuss certain aspects of passivity results in dynamic systems and the characterization of the regenerative systems counterparts. In particular, the various concepts of passivity as standard passivity, strict input passivity, strict output passivity, and very strict passivity (i.e., joint strict input and output passivity) are given and related to the existence of a storage function and a dissipation function. Later on, the obtained results are related to external positivity of systems and positivity or strict positivity of the transfer matrices and transfer functions in the time-invariant case. On the other hand, how to achieve or how eventually to increase the passivity effects via linear feedback by the synthesis of the appropriate feed-forward or feedback controllers or, simply, by adding a positive parallel direct input-output matrix interconnection gain is discussed.http://dx.doi.org/10.1155/2018/5298756 |
| spellingShingle | M. De la Sen On the Passivity and Positivity Properties in Dynamic Systems: Their Achievement under Control Laws and Their Maintenance under Parameterizations Switching Journal of Mathematics |
| title | On the Passivity and Positivity Properties in Dynamic Systems: Their Achievement under Control Laws and Their Maintenance under Parameterizations Switching |
| title_full | On the Passivity and Positivity Properties in Dynamic Systems: Their Achievement under Control Laws and Their Maintenance under Parameterizations Switching |
| title_fullStr | On the Passivity and Positivity Properties in Dynamic Systems: Their Achievement under Control Laws and Their Maintenance under Parameterizations Switching |
| title_full_unstemmed | On the Passivity and Positivity Properties in Dynamic Systems: Their Achievement under Control Laws and Their Maintenance under Parameterizations Switching |
| title_short | On the Passivity and Positivity Properties in Dynamic Systems: Their Achievement under Control Laws and Their Maintenance under Parameterizations Switching |
| title_sort | on the passivity and positivity properties in dynamic systems their achievement under control laws and their maintenance under parameterizations switching |
| url | http://dx.doi.org/10.1155/2018/5298756 |
| work_keys_str_mv | AT mdelasen onthepassivityandpositivitypropertiesindynamicsystemstheirachievementundercontrollawsandtheirmaintenanceunderparameterizationsswitching |