### 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 | 9th IFAC Workshop on Time Delay Systems, TDS 2010 - Proceedings |

Pages | 138-143 |

Number of pages | 6 |

Edition | PART 1 |

State | Published - Dec 1 2010 |

Externally published | Yes |

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

### Publication series

Name | IFAC Proceedings Volumes (IFAC-PapersOnline) |
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Number | PART 1 |

ISSN (Print) | 1474-6670 |

### 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 |

### Keywords

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

### ASJC Scopus subject areas

- Control and Systems Engineering

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## Cite this

Gu, K., Zhang, Y., & Peet, M. (2010). Accelerating convergence of sum-of-square stability analysis of coupled differential-difference equations. In

*9th IFAC Workshop on Time Delay Systems, TDS 2010 - Proceedings*(PART 1 ed., pp. 138-143). (IFAC Proceedings Volumes (IFAC-PapersOnline); No. PART 1).