### Abstract

This article aims at accelerating the convergence of Lyapunov-Krasovskii stability analysis of coupled differential-difference equations using sum-of-square formulation. Under the assumption that the single integral and double integral terms are both positive definite, a necessary and sufficient condition for the quadratic integral expression is obtained. This result is applied to the Lyapunov-Krasovskii functional and derivative conditions. The method is less conservative than the previous method with identical order of polynomials. The effectiveness of this method is illustrated by numerical examples.

Original language | English (US) |
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Title of host publication | IFAC Proceedings Volumes (IFAC-PapersOnline) |

Pages | 138-143 |

Number of pages | 6 |

Edition | PART 1 |

State | Published - 2010 |

Externally published | Yes |

Event | 9th IFAC Workshop on Time Delay Systems, TDS 2010 - Prague, Czech Republic Duration: Jun 7 2010 → Jun 9 2010 |

### Other

Other | 9th IFAC Workshop on Time Delay Systems, TDS 2010 |
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Country | Czech Republic |

City | Prague |

Period | 6/7/10 → 6/9/10 |

### Fingerprint

### Keywords

- Delay
- Lyapunov-krasovskii functional
- Sum-of-square

### ASJC Scopus subject areas

- Control and Systems Engineering

### Cite this

*IFAC Proceedings Volumes (IFAC-PapersOnline)*(PART 1 ed., pp. 138-143)

**Accelerating convergence of sum-of-square stability analysis of coupled differential-difference equations.** / Gu, Keqin; Zhang, Yashun; Peet, Matthew.

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

*IFAC Proceedings Volumes (IFAC-PapersOnline).*PART 1 edn, pp. 138-143, 9th IFAC Workshop on Time Delay Systems, TDS 2010, Prague, Czech Republic, 6/7/10.

}

TY - GEN

T1 - Accelerating convergence of sum-of-square stability analysis of coupled differential-difference equations

AU - Gu, Keqin

AU - Zhang, Yashun

AU - Peet, Matthew

PY - 2010

Y1 - 2010

N2 - This article aims at accelerating the convergence of Lyapunov-Krasovskii stability analysis of coupled differential-difference equations using sum-of-square formulation. Under the assumption that the single integral and double integral terms are both positive definite, a necessary and sufficient condition for the quadratic integral expression is obtained. This result is applied to the Lyapunov-Krasovskii functional and derivative conditions. The method is less conservative than the previous method with identical order of polynomials. The effectiveness of this method is illustrated by numerical examples.

AB - This article aims at accelerating the convergence of Lyapunov-Krasovskii stability analysis of coupled differential-difference equations using sum-of-square formulation. Under the assumption that the single integral and double integral terms are both positive definite, a necessary and sufficient condition for the quadratic integral expression is obtained. This result is applied to the Lyapunov-Krasovskii functional and derivative conditions. The method is less conservative than the previous method with identical order of polynomials. The effectiveness of this method is illustrated by numerical examples.

KW - Delay

KW - Lyapunov-krasovskii functional

KW - Sum-of-square

UR - http://www.scopus.com/inward/record.url?scp=84871365189&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84871365189&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:84871365189

SN - 9783902661715

SP - 138

EP - 143

BT - IFAC Proceedings Volumes (IFAC-PapersOnline)

ER -