### Abstract

This paper studies LMI-based robust performance analysis of linear time-invariant systems depending on uncertain parameters. In the case where the coefficient matrices of the system are affine with respect to the uncertain parameters, the standard LMI's are helpful in dealing with such analysis problems provided that we accept the notion of quadratic stability. On the other hand, in the case of rational parameter dependence, the standard LMI's carry some deficiency and thus we need another effort to derive numerically tractable conditions. This paper shows that recently developed dilated LMI's are effective in attacking such robust performance analysis problems. Indeed, applying dilated LMI's leads directly to numerically tractable conditions regardless of the form of the dependence on uncertain parameters. In addition, dilated LMI's enable us to employ parameter-dependent Lyapunov variables to test robust performance, which are known to be quite effective to alleviate the conservatism resulting from a quadratic (parameter-independent) Lyapunov variable.

Original language | English |
---|---|

Pages (from-to) | 839-844 |

Number of pages | 6 |

Journal | Proceedings of the American Control Conference |

Volume | 1 |

Publication status | Published - Nov 6 2003 |

Externally published | Yes |

Event | 2003 American Control Conference - Denver, CO, United States Duration: Jun 4 2003 → Jun 6 2003 |

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### All Science Journal Classification (ASJC) codes

- Electrical and Electronic Engineering

### Cite this

*Proceedings of the American Control Conference*,

*1*, 839-844.

**A Dilated LMI Approach to Robust Performance Analysis of Linear Time-Invariant Uncertain Systems.** / Ebihara, Yoshio; Hagiwara, Tomomichi.

Research output: Contribution to journal › Conference article

*Proceedings of the American Control Conference*, vol. 1, pp. 839-844.

}

TY - JOUR

T1 - A Dilated LMI Approach to Robust Performance Analysis of Linear Time-Invariant Uncertain Systems

AU - Ebihara, Yoshio

AU - Hagiwara, Tomomichi

PY - 2003/11/6

Y1 - 2003/11/6

N2 - This paper studies LMI-based robust performance analysis of linear time-invariant systems depending on uncertain parameters. In the case where the coefficient matrices of the system are affine with respect to the uncertain parameters, the standard LMI's are helpful in dealing with such analysis problems provided that we accept the notion of quadratic stability. On the other hand, in the case of rational parameter dependence, the standard LMI's carry some deficiency and thus we need another effort to derive numerically tractable conditions. This paper shows that recently developed dilated LMI's are effective in attacking such robust performance analysis problems. Indeed, applying dilated LMI's leads directly to numerically tractable conditions regardless of the form of the dependence on uncertain parameters. In addition, dilated LMI's enable us to employ parameter-dependent Lyapunov variables to test robust performance, which are known to be quite effective to alleviate the conservatism resulting from a quadratic (parameter-independent) Lyapunov variable.

AB - This paper studies LMI-based robust performance analysis of linear time-invariant systems depending on uncertain parameters. In the case where the coefficient matrices of the system are affine with respect to the uncertain parameters, the standard LMI's are helpful in dealing with such analysis problems provided that we accept the notion of quadratic stability. On the other hand, in the case of rational parameter dependence, the standard LMI's carry some deficiency and thus we need another effort to derive numerically tractable conditions. This paper shows that recently developed dilated LMI's are effective in attacking such robust performance analysis problems. Indeed, applying dilated LMI's leads directly to numerically tractable conditions regardless of the form of the dependence on uncertain parameters. In addition, dilated LMI's enable us to employ parameter-dependent Lyapunov variables to test robust performance, which are known to be quite effective to alleviate the conservatism resulting from a quadratic (parameter-independent) Lyapunov variable.

UR - http://www.scopus.com/inward/record.url?scp=0142248123&partnerID=8YFLogxK

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M3 - Conference article

AN - SCOPUS:0142248123

VL - 1

SP - 839

EP - 844

JO - Proceedings of the American Control Conference

JF - Proceedings of the American Control Conference

SN - 0743-1619

ER -