Geometric techniques for implicit two-dimensional systems
Geometric tools are developed for two-dimensional (2-D) models in an implicitFornasini–Marchesini form. In particular, the structural properties of controlled and conditionedinvariance are defined and studied. These properties are investigated in terms ofquarter-plane causal solutions of the implici...
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| Format: | Journal Article |
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Springer Netherlands
2013
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| Online Access: | http://hdl.handle.net/20.500.11937/13089 |
| _version_ | 1848748255284822016 |
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| author | Ntogramatzidis, Lorenzo Cantoni, Michael |
| author2 | Romero G.E. |
| author_facet | Romero G.E. Ntogramatzidis, Lorenzo Cantoni, Michael |
| author_sort | Ntogramatzidis, Lorenzo |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | Geometric tools are developed for two-dimensional (2-D) models in an implicitFornasini–Marchesini form. In particular, the structural properties of controlled and conditionedinvariance are defined and studied. These properties are investigated in terms ofquarter-plane causal solutions of the implicit model given compatible boundary conditions.The definitions of controlled and conditioned invariance introduced, along with the correspondingoutput-nulling and input-containing subspaces, are shown to be richer than theone-dimensional counterparts. The analysis carried out in this paper establishes necessaryand sufficient conditions for the solvability of 2-D disturbance decoupling problems andunknown-input observation problems. The conditions obtained are expressed in terms ofoutput-nulling and input-containing subspaces, which can be computed recursively in a finitenumber of steps. |
| first_indexed | 2025-11-14T07:02:08Z |
| format | Journal Article |
| id | curtin-20.500.11937-13089 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T07:02:08Z |
| publishDate | 2013 |
| publisher | Springer Netherlands |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-130892023-02-07T08:01:25Z Geometric techniques for implicit two-dimensional systems Ntogramatzidis, Lorenzo Cantoni, Michael Romero G.E. Sunyaev R.A. Sunyaev R.A. Belloni T.M. Two-dimensional systems Implicit Fornasini–Marchesini models Controlled and conditioned invariance Geometric tools are developed for two-dimensional (2-D) models in an implicitFornasini–Marchesini form. In particular, the structural properties of controlled and conditionedinvariance are defined and studied. These properties are investigated in terms ofquarter-plane causal solutions of the implicit model given compatible boundary conditions.The definitions of controlled and conditioned invariance introduced, along with the correspondingoutput-nulling and input-containing subspaces, are shown to be richer than theone-dimensional counterparts. The analysis carried out in this paper establishes necessaryand sufficient conditions for the solvability of 2-D disturbance decoupling problems andunknown-input observation problems. The conditions obtained are expressed in terms ofoutput-nulling and input-containing subspaces, which can be computed recursively in a finitenumber of steps. 2013 Journal Article http://hdl.handle.net/20.500.11937/13089 10.1007/s11045-012-0205-4 Springer Netherlands fulltext |
| spellingShingle | Two-dimensional systems Implicit Fornasini–Marchesini models Controlled and conditioned invariance Ntogramatzidis, Lorenzo Cantoni, Michael Geometric techniques for implicit two-dimensional systems |
| title | Geometric techniques for implicit two-dimensional systems |
| title_full | Geometric techniques for implicit two-dimensional systems |
| title_fullStr | Geometric techniques for implicit two-dimensional systems |
| title_full_unstemmed | Geometric techniques for implicit two-dimensional systems |
| title_short | Geometric techniques for implicit two-dimensional systems |
| title_sort | geometric techniques for implicit two-dimensional systems |
| topic | Two-dimensional systems Implicit Fornasini–Marchesini models Controlled and conditioned invariance |
| url | http://hdl.handle.net/20.500.11937/13089 |