### Abstract

This paper addresses robust D-stability analysis problems of uncertain polynomial matrices. The underlying idea we follow is that a given polynomial matrix is D-stable if and only if there exist polynomial-type multipliers that render the resulting polynomial matrices to be strictly positive over a specific region on the complex plane. By applying the generalized S-procedure technique, we show that those positivity analysis problems can be reduced into feasibility tests of linear matrix inequalities (LMIs). Thus we can obtain varieties of LMI conditions for (robust) D-stability analysis of polynomial matrices according to the degree/structure of the multipliers to be employed. in particular, we show that existing LMI conditions for robust D-stability analysis can be viewed as particular cases of the proposed conditions, where the degree of the multipliers chosen to be the same as those of the polynomial matrices to be examined. It turns out that, by increasing the degree of the multipliers, we can readily obtain less conservative LMI conditions than the one found in the literature.

Original language | English |
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Title of host publication | Proceedings of the 16th IFAC World Congress, IFAC 2005 |

Pages | 191-196 |

Number of pages | 6 |

Publication status | Published - Dec 1 2005 |

Externally published | Yes |

Event | 16th Triennial World Congress of International Federation of Automatic Control, IFAC 2005 - Prague, Czech Republic Duration: Jul 3 2005 → Jul 8 2005 |

### Publication series

Name | IFAC Proceedings Volumes (IFAC-PapersOnline) |
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Volume | 16 |

ISSN (Print) | 1474-6670 |

### Conference

Conference | 16th Triennial World Congress of International Federation of Automatic Control, IFAC 2005 |
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Country | Czech Republic |

City | Prague |

Period | 7/3/05 → 7/8/05 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Control and Systems Engineering

### Cite this

*Proceedings of the 16th IFAC World Congress, IFAC 2005*(pp. 191-196). (IFAC Proceedings Volumes (IFAC-PapersOnline); Vol. 16).

**Robust D-stability analysis of uncertain polynomial matrices via polynomial-type multipliers.** / Ebihara, Yoshio; Maeda, Katsutoshi; Hagiwara, Tomomichi.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings of the 16th IFAC World Congress, IFAC 2005.*IFAC Proceedings Volumes (IFAC-PapersOnline), vol. 16, pp. 191-196, 16th Triennial World Congress of International Federation of Automatic Control, IFAC 2005, Prague, Czech Republic, 7/3/05.

}

TY - GEN

T1 - Robust D-stability analysis of uncertain polynomial matrices via polynomial-type multipliers

AU - Ebihara, Yoshio

AU - Maeda, Katsutoshi

AU - Hagiwara, Tomomichi

PY - 2005/12/1

Y1 - 2005/12/1

N2 - This paper addresses robust D-stability analysis problems of uncertain polynomial matrices. The underlying idea we follow is that a given polynomial matrix is D-stable if and only if there exist polynomial-type multipliers that render the resulting polynomial matrices to be strictly positive over a specific region on the complex plane. By applying the generalized S-procedure technique, we show that those positivity analysis problems can be reduced into feasibility tests of linear matrix inequalities (LMIs). Thus we can obtain varieties of LMI conditions for (robust) D-stability analysis of polynomial matrices according to the degree/structure of the multipliers to be employed. in particular, we show that existing LMI conditions for robust D-stability analysis can be viewed as particular cases of the proposed conditions, where the degree of the multipliers chosen to be the same as those of the polynomial matrices to be examined. It turns out that, by increasing the degree of the multipliers, we can readily obtain less conservative LMI conditions than the one found in the literature.

AB - This paper addresses robust D-stability analysis problems of uncertain polynomial matrices. The underlying idea we follow is that a given polynomial matrix is D-stable if and only if there exist polynomial-type multipliers that render the resulting polynomial matrices to be strictly positive over a specific region on the complex plane. By applying the generalized S-procedure technique, we show that those positivity analysis problems can be reduced into feasibility tests of linear matrix inequalities (LMIs). Thus we can obtain varieties of LMI conditions for (robust) D-stability analysis of polynomial matrices according to the degree/structure of the multipliers to be employed. in particular, we show that existing LMI conditions for robust D-stability analysis can be viewed as particular cases of the proposed conditions, where the degree of the multipliers chosen to be the same as those of the polynomial matrices to be examined. It turns out that, by increasing the degree of the multipliers, we can readily obtain less conservative LMI conditions than the one found in the literature.

UR - http://www.scopus.com/inward/record.url?scp=79960738380&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79960738380&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:79960738380

SN - 008045108X

SN - 9780080451084

T3 - IFAC Proceedings Volumes (IFAC-PapersOnline)

SP - 191

EP - 196

BT - Proceedings of the 16th IFAC World Congress, IFAC 2005

ER -