How scaling of the disturbance set affects robust positively invariant sets for linear systems
This paper presents new results on robust positively invariant (RPI) sets for linear discrete-time systems with additive disturbances. In particular, we study how RPI sets change with scaling of the disturbance set. More precisely, we show that many properties of RPI sets crucially depend on a uniqu...
| Main Authors: | , , |
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| Format: | Journal article |
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Wiley
2017
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| _version_ | 1797055769137381376 |
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| author | Schulze Darup, M Schaich, R Cannon, M |
| author_facet | Schulze Darup, M Schaich, R Cannon, M |
| author_sort | Schulze Darup, M |
| collection | OXFORD |
| description | This paper presents new results on robust positively invariant (RPI) sets for linear discrete-time systems with additive disturbances. In particular, we study how RPI sets change with scaling of the disturbance set. More precisely, we show that many properties of RPI sets crucially depend on a unique scaling factor, which determines the transition from nonempty to empty RPI sets. We characterize this critical scaling factor, present an efficient algorithm for its computation, and analyze it for a number of examples from the literature. |
| first_indexed | 2024-03-06T19:14:31Z |
| format | Journal article |
| id | oxford-uuid:17e3941d-595c-4efa-8387-39fe8ce535bc |
| institution | University of Oxford |
| last_indexed | 2024-03-06T19:14:31Z |
| publishDate | 2017 |
| publisher | Wiley |
| record_format | dspace |
| spelling | oxford-uuid:17e3941d-595c-4efa-8387-39fe8ce535bc2022-03-26T10:40:07ZHow scaling of the disturbance set affects robust positively invariant sets for linear systemsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:17e3941d-595c-4efa-8387-39fe8ce535bcSymplectic Elements at OxfordWiley2017Schulze Darup, MSchaich, RCannon, MThis paper presents new results on robust positively invariant (RPI) sets for linear discrete-time systems with additive disturbances. In particular, we study how RPI sets change with scaling of the disturbance set. More precisely, we show that many properties of RPI sets crucially depend on a unique scaling factor, which determines the transition from nonempty to empty RPI sets. We characterize this critical scaling factor, present an efficient algorithm for its computation, and analyze it for a number of examples from the literature. |
| spellingShingle | Schulze Darup, M Schaich, R Cannon, M How scaling of the disturbance set affects robust positively invariant sets for linear systems |
| title | How scaling of the disturbance set affects robust positively invariant sets for linear systems |
| title_full | How scaling of the disturbance set affects robust positively invariant sets for linear systems |
| title_fullStr | How scaling of the disturbance set affects robust positively invariant sets for linear systems |
| title_full_unstemmed | How scaling of the disturbance set affects robust positively invariant sets for linear systems |
| title_short | How scaling of the disturbance set affects robust positively invariant sets for linear systems |
| title_sort | how scaling of the disturbance set affects robust positively invariant sets for linear systems |
| work_keys_str_mv | AT schulzedarupm howscalingofthedisturbancesetaffectsrobustpositivelyinvariantsetsforlinearsystems AT schaichr howscalingofthedisturbancesetaffectsrobustpositivelyinvariantsetsforlinearsystems AT cannonm howscalingofthedisturbancesetaffectsrobustpositivelyinvariantsetsforlinearsystems |