### Abstract

We present an algorithmic methodology for constructing Lyapunov-Krasovskii (L-K) functionals for linear time-delay systems, using the sum of squares decomposition of multivariate polynomials to solve the related infinite dimensional Linear Matrix Inequalities (LMIs). The resulting functionals retain the structure of the complete L-K functional and yield conditions that approach the true delay-dependent stability bounds. The method can also be used to construct parameter-dependent L-K functionals for certifying stability under parametric uncertainty.

Original language | English (US) |
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Title of host publication | Proceedings of the American Control Conference |

Pages | 2845-2850 |

Number of pages | 6 |

Volume | 4 |

State | Published - 2005 |

Externally published | Yes |

Event | 2005 American Control Conference, ACC - Portland, OR, United States Duration: Jun 8 2005 → Jun 10 2005 |

### Other

Other | 2005 American Control Conference, ACC |
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Country | United States |

City | Portland, OR |

Period | 6/8/05 → 6/10/05 |

### Fingerprint

### ASJC Scopus subject areas

- Control and Systems Engineering

### Cite this

*Proceedings of the American Control Conference*(Vol. 4, pp. 2845-2850)

**Constructing Lyapunov-Krasovskii functionals for linear time delay systems.** / Papachristodoulou, Antonis; Peet, Matthew; Lall, Sanjay.

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

*Proceedings of the American Control Conference.*vol. 4, pp. 2845-2850, 2005 American Control Conference, ACC, Portland, OR, United States, 6/8/05.

}

TY - GEN

T1 - Constructing Lyapunov-Krasovskii functionals for linear time delay systems

AU - Papachristodoulou, Antonis

AU - Peet, Matthew

AU - Lall, Sanjay

PY - 2005

Y1 - 2005

N2 - We present an algorithmic methodology for constructing Lyapunov-Krasovskii (L-K) functionals for linear time-delay systems, using the sum of squares decomposition of multivariate polynomials to solve the related infinite dimensional Linear Matrix Inequalities (LMIs). The resulting functionals retain the structure of the complete L-K functional and yield conditions that approach the true delay-dependent stability bounds. The method can also be used to construct parameter-dependent L-K functionals for certifying stability under parametric uncertainty.

AB - We present an algorithmic methodology for constructing Lyapunov-Krasovskii (L-K) functionals for linear time-delay systems, using the sum of squares decomposition of multivariate polynomials to solve the related infinite dimensional Linear Matrix Inequalities (LMIs). The resulting functionals retain the structure of the complete L-K functional and yield conditions that approach the true delay-dependent stability bounds. The method can also be used to construct parameter-dependent L-K functionals for certifying stability under parametric uncertainty.

UR - http://www.scopus.com/inward/record.url?scp=23944516367&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=23944516367&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:23944516367

VL - 4

SP - 2845

EP - 2850

BT - Proceedings of the American Control Conference

ER -