### Abstract

This paper considers the problem of reducing the computational complexity associated with the Sum-of-Squares approach to stability analysis of time-delay systems. Specifically, this paper considers systems with a large state-space but with relatively few delays-the most common situation in practice. The paper uses the general framework of coupled differential-difference equations with delays in low-dimensional feedback channels. This framework includes both the standard delayed and neutral-type systems. The approach is based on recent results which introduced a new type of Lyapunov-Krasovskii form which was shown to be necessary and sufficient for stability of this class of systems. This paper shows how exploiting the structure of the new functional can yield dramatic improvements in computational complexity. Numerical examples are given to illustrate this improvement.

Original language | English (US) |
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Title of host publication | Proceedings of the 2010 American Control Conference, ACC 2010 |

Pages | 5018-5023 |

Number of pages | 6 |

State | Published - Oct 15 2010 |

Externally published | Yes |

Event | 2010 American Control Conference, ACC 2010 - Baltimore, MD, United States Duration: Jun 30 2010 → Jul 2 2010 |

### Publication series

Name | Proceedings of the 2010 American Control Conference, ACC 2010 |
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### Other

Other | 2010 American Control Conference, ACC 2010 |
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Country | United States |

City | Baltimore, MD |

Period | 6/30/10 → 7/2/10 |

### Keywords

- Complexity
- Lyapunov-krasovskii
- Semidefinite programming
- Sum-of-squares
- Time delay

### ASJC Scopus subject areas

- Control and Systems Engineering

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## Cite this

*Proceedings of the 2010 American Control Conference, ACC 2010*(pp. 5018-5023). [5530749] (Proceedings of the 2010 American Control Conference, ACC 2010).