Solvability conditions for the positive real lemma equations in the discrete time
Passivity theory and the positive real lemma have been recognised as two of the cornerstones of modern systems and control theory. As digital control is pervasive in virtually all control applications, developing a general theory on the discretetime positive real lemma appears to be an important iss...
| Main Authors: | , |
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| Format: | Journal Article |
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The Institution of Engineering and Technology
2017
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| Online Access: | http://hdl.handle.net/20.500.11937/57714 |
| _version_ | 1848760077768458240 |
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| author | Ferrante, A. Ntogramatzidis, Lorenzo |
| author_facet | Ferrante, A. Ntogramatzidis, Lorenzo |
| author_sort | Ferrante, A. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | Passivity theory and the positive real lemma have been recognised as two of the cornerstones of modern systems and control theory. As digital control is pervasive in virtually all control applications, developing a general theory on the discretetime positive real lemma appears to be an important issue. While for minimal realisations the relations between passivity, positive-realness and existence of solutions of the positive real lemma equations is very well understood, it seems fair to say that this is not the case in the discrete-time case, especially when the realisation is non-minimal and no conditions are assumed on left-and/or right-invertibility of the transfer function. The purpose of this study is to present a necessary and sufficient condition for existence of solutions of the positive real equations under the only assumption that the state matrix A is asymptotically stable. |
| first_indexed | 2025-11-14T10:10:03Z |
| format | Journal Article |
| id | curtin-20.500.11937-57714 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T10:10:03Z |
| publishDate | 2017 |
| publisher | The Institution of Engineering and Technology |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-577142018-02-20T05:41:08Z Solvability conditions for the positive real lemma equations in the discrete time Ferrante, A. Ntogramatzidis, Lorenzo Passivity theory and the positive real lemma have been recognised as two of the cornerstones of modern systems and control theory. As digital control is pervasive in virtually all control applications, developing a general theory on the discretetime positive real lemma appears to be an important issue. While for minimal realisations the relations between passivity, positive-realness and existence of solutions of the positive real lemma equations is very well understood, it seems fair to say that this is not the case in the discrete-time case, especially when the realisation is non-minimal and no conditions are assumed on left-and/or right-invertibility of the transfer function. The purpose of this study is to present a necessary and sufficient condition for existence of solutions of the positive real equations under the only assumption that the state matrix A is asymptotically stable. 2017 Journal Article http://hdl.handle.net/20.500.11937/57714 10.1049/iet-cta.2017.0314 The Institution of Engineering and Technology restricted |
| spellingShingle | Ferrante, A. Ntogramatzidis, Lorenzo Solvability conditions for the positive real lemma equations in the discrete time |
| title | Solvability conditions for the positive real lemma equations in the discrete time |
| title_full | Solvability conditions for the positive real lemma equations in the discrete time |
| title_fullStr | Solvability conditions for the positive real lemma equations in the discrete time |
| title_full_unstemmed | Solvability conditions for the positive real lemma equations in the discrete time |
| title_short | Solvability conditions for the positive real lemma equations in the discrete time |
| title_sort | solvability conditions for the positive real lemma equations in the discrete time |
| url | http://hdl.handle.net/20.500.11937/57714 |