## On stabilizability-holdability problem for linear discrete time systems

dc.contributor.author | Rumchev, Ventseslav | |

dc.contributor.author | Higashiyama, Y. | |

dc.date.accessioned | 2017-01-30T11:50:47Z | |

dc.date.available | 2017-01-30T11:50:47Z | |

dc.date.created | 2012-03-23T01:19:49Z | |

dc.date.issued | 2011 | |

dc.identifier.citation | Rumchev, Ventsi George and Higashiyama, Yoichi. 2011. On stabilizability-holdability problem for linear discrete time systems. Systems Science. 36 (2): pp. 33-38. | |

dc.identifier.uri | http://hdl.handle.net/20.500.11937/15606 | |

dc.description.abstract |
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. | |

dc.publisher | Oficyna Wydawnicza Politechniki Wroclawskiej | |

dc.title | On stabilizability-holdability problem for linear discrete time systems | |

dc.type | Journal Article | |

dcterms.source.volume | 36 | |

dcterms.source.startPage | 33 | |

dcterms.source.endPage | 38 | |

dcterms.source.issn | 01371223 | |

dcterms.source.title | Systems Science | |

curtin.department | Department of Mathematics and Statistics | |

curtin.accessStatus | Fulltext not available |