### Abstract

This technical note considers the problem of reducing the computational complexity associated with the Sum-of-Squares approach to stability analysis of time-delay systems. Specifically, this technical note considers systems with a large state-space but where delays affect only certain parts of the system. This yields a coefficient matrix of the delayed state with low ranka common scenario in practice. The technical note uses the general framework of coupled differential-difference equations with delays in feedback channels. This framework includes systems of both the neutral and retarded-type. The approach is based on recent results which introduced a new LyapunovKrasovskii structure which was shown to be necessary and sufficient for stability of this class of systems. This technical note 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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Article number | 5605235 |

Pages (from-to) | 229-234 |

Number of pages | 6 |

Journal | IEEE Transactions on Automatic Control |

Volume | 56 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1 2011 |

Externally published | Yes |

### Keywords

- Complexity
- LyapunovKrasovskii functional
- semi definite programming
- sum-of-squares
- time delay

### ASJC Scopus subject areas

- Control and Systems Engineering
- Computer Science Applications
- Electrical and Electronic Engineering

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## Cite this

*IEEE Transactions on Automatic Control*,

*56*(1), 229-234. [5605235]. https://doi.org/10.1109/TAC.2010.2088590