### Abstract

In this paper, we propose novel eigenstructure assignment method in full-state feedback for linear time-invariant MIMO system such that directions of some left eigenvectors are exactly assigned to the desired directions. It is required to consider the direction of left eigenvector in designing eigenstructure of closed-loop system, because the direction of left eigenvector has influence over excitation by associated input variables in time-domain response. Exact direction of a left eigenvector can be achieved by assigning proper right eigenvector set satisfying the conditions of the presented theorem based on Moore's theorem and the orthogonality of left and right eigenvector. The right eigenvector should reside in the subspace given by the desired eigenvalue, which restrict a number of designable left eigenvector. For the two cases in which desired eigenvalues are all real and contain complex number, design freedom of designable left eigenvector are given.

Original language | English |
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Pages (from-to) | 226-231 |

Number of pages | 6 |

Journal | Journal of Institute of Control, Robotics and Systems |

Volume | 14 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2008 Mar 1 |

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### All Science Journal Classification (ASJC) codes

- Software
- Control and Systems Engineering
- Applied Mathematics

### Cite this

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*Journal of Institute of Control, Robotics and Systems*, vol. 14, no. 3, pp. 226-231. https://doi.org/10.5302/J.ICROS.2008.14.3.226

**Direction assignment of left eigenvector in linear MIMO system.** / Kim, Sung Hyun; Yang, Hyun Seok.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Direction assignment of left eigenvector in linear MIMO system

AU - Kim, Sung Hyun

AU - Yang, Hyun Seok

PY - 2008/3/1

Y1 - 2008/3/1

N2 - In this paper, we propose novel eigenstructure assignment method in full-state feedback for linear time-invariant MIMO system such that directions of some left eigenvectors are exactly assigned to the desired directions. It is required to consider the direction of left eigenvector in designing eigenstructure of closed-loop system, because the direction of left eigenvector has influence over excitation by associated input variables in time-domain response. Exact direction of a left eigenvector can be achieved by assigning proper right eigenvector set satisfying the conditions of the presented theorem based on Moore's theorem and the orthogonality of left and right eigenvector. The right eigenvector should reside in the subspace given by the desired eigenvalue, which restrict a number of designable left eigenvector. For the two cases in which desired eigenvalues are all real and contain complex number, design freedom of designable left eigenvector are given.

AB - In this paper, we propose novel eigenstructure assignment method in full-state feedback for linear time-invariant MIMO system such that directions of some left eigenvectors are exactly assigned to the desired directions. It is required to consider the direction of left eigenvector in designing eigenstructure of closed-loop system, because the direction of left eigenvector has influence over excitation by associated input variables in time-domain response. Exact direction of a left eigenvector can be achieved by assigning proper right eigenvector set satisfying the conditions of the presented theorem based on Moore's theorem and the orthogonality of left and right eigenvector. The right eigenvector should reside in the subspace given by the desired eigenvalue, which restrict a number of designable left eigenvector. For the two cases in which desired eigenvalues are all real and contain complex number, design freedom of designable left eigenvector are given.

UR - http://www.scopus.com/inward/record.url?scp=58149101800&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=58149101800&partnerID=8YFLogxK

U2 - 10.5302/J.ICROS.2008.14.3.226

DO - 10.5302/J.ICROS.2008.14.3.226

M3 - Article

AN - SCOPUS:58149101800

VL - 14

SP - 226

EP - 231

JO - Journal of Institute of Control, Robotics and Systems

JF - Journal of Institute of Control, Robotics and Systems

SN - 1976-5622

IS - 3

ER -