### 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) |
---|---|

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 2011 |

Externally published | Yes |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

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

### Cite this

*IEEE Transactions on Automatic Control*,

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

**Reducing the complexity of the sum-of-squares test for stability of delayed linear systems.** / Zhang, Yashun; Peet, Matthew; Gu, Keqin.

Research output: Contribution to journal › Article

*IEEE Transactions on Automatic Control*, vol. 56, no. 1, 5605235, pp. 229-234. https://doi.org/10.1109/TAC.2010.2088590

}

TY - JOUR

T1 - Reducing the complexity of the sum-of-squares test for stability of delayed linear systems

AU - Zhang, Yashun

AU - Peet, Matthew

AU - Gu, Keqin

PY - 2011/1

Y1 - 2011/1

N2 - 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.

AB - 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.

KW - Complexity

KW - LyapunovKrasovskii functional

KW - semi definite programming

KW - sum-of-squares

KW - time delay

UR - http://www.scopus.com/inward/record.url?scp=78651312622&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=78651312622&partnerID=8YFLogxK

U2 - 10.1109/TAC.2010.2088590

DO - 10.1109/TAC.2010.2088590

M3 - Article

AN - SCOPUS:78651312622

VL - 56

SP - 229

EP - 234

JO - IEEE Transactions on Automatic Control

JF - IEEE Transactions on Automatic Control

SN - 0018-9286

IS - 1

M1 - 5605235

ER -