On stabilizability-holdability problem for linear discrete time systems
Consider the following problem. Given a linear discrete-time system, find if possible a linear state-feedback control law such that under this law all system trajectories originating in the non-negative orthant remain non-negative while asymptotically converging to the origin. This problem is called...
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| Format: | Journal Article |
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Oficyna Wydawnicza Politechniki Wroclawskiej
2011
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| Online Access: | http://hdl.handle.net/20.500.11937/15606 |
| _version_ | 1848748938876682240 |
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| author | Rumchev, Ventseslav Higashiyama, Y. |
| author_facet | Rumchev, Ventseslav Higashiyama, Y. |
| author_sort | Rumchev, Ventseslav |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | Consider the following problem. Given a linear discrete-time system, find if possible a linear state-feedback control law such that under this law all system trajectories originating in the non-negative orthant remain non-negative while asymptotically converging to the origin. This problem is called feedback stabilizability-holdabiltiy problem (FSH). If, in addition, the requirement of non-negativity is imposed on the controls, the problem is a positive feedback stabilizability-holdabiltiy problem (PFSH). It is shown that the set of all linear state feedback controllers that make the open-loop system holdable and asymptotically stable is a polyhedron and the external representation of this polyhedron is obtained. Necessary and sufficient conditions for identifying when the open-loop system is not positive feedback R+n-invariant (and therefore there is no solution to the PFSH problem) are obtained in terms of the system parameters. A constructive linear programming based approach to the solution of FSH and PFSH problems is developed in the paper. This approach provides not only a simple computational procedure to find out whether the FSF, respectively the PFSH problem, has a solution or not but also to determine a linear state feedback controller (respectively, a non-negative linear state feedback controller) that endows the closed-loop (positive) system with a maximum stability margin and guarantees the fastest possible convergence to the origin. |
| first_indexed | 2025-11-14T07:13:00Z |
| format | Journal Article |
| id | curtin-20.500.11937-15606 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T07:13:00Z |
| publishDate | 2011 |
| publisher | Oficyna Wydawnicza Politechniki Wroclawskiej |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-156062017-03-08T13:10:09Z On stabilizability-holdability problem for linear discrete time systems Rumchev, Ventseslav Higashiyama, Y. Consider the following problem. Given a linear discrete-time system, find if possible a linear state-feedback control law such that under this law all system trajectories originating in the non-negative orthant remain non-negative while asymptotically converging to the origin. This problem is called feedback stabilizability-holdabiltiy problem (FSH). If, in addition, the requirement of non-negativity is imposed on the controls, the problem is a positive feedback stabilizability-holdabiltiy problem (PFSH). It is shown that the set of all linear state feedback controllers that make the open-loop system holdable and asymptotically stable is a polyhedron and the external representation of this polyhedron is obtained. Necessary and sufficient conditions for identifying when the open-loop system is not positive feedback R+n-invariant (and therefore there is no solution to the PFSH problem) are obtained in terms of the system parameters. A constructive linear programming based approach to the solution of FSH and PFSH problems is developed in the paper. This approach provides not only a simple computational procedure to find out whether the FSF, respectively the PFSH problem, has a solution or not but also to determine a linear state feedback controller (respectively, a non-negative linear state feedback controller) that endows the closed-loop (positive) system with a maximum stability margin and guarantees the fastest possible convergence to the origin. 2011 Journal Article http://hdl.handle.net/20.500.11937/15606 Oficyna Wydawnicza Politechniki Wroclawskiej restricted |
| spellingShingle | Rumchev, Ventseslav Higashiyama, Y. On stabilizability-holdability problem for linear discrete time systems |
| title | On stabilizability-holdability problem for linear discrete time systems |
| title_full | On stabilizability-holdability problem for linear discrete time systems |
| title_fullStr | On stabilizability-holdability problem for linear discrete time systems |
| title_full_unstemmed | On stabilizability-holdability problem for linear discrete time systems |
| title_short | On stabilizability-holdability problem for linear discrete time systems |
| title_sort | on stabilizability-holdability problem for linear discrete time systems |
| url | http://hdl.handle.net/20.500.11937/15606 |