## Abstract

A linear delayed vector equation x(t)=∑k=1^m A_k(t)x(h_k(t)), tin [0,∞ ) is investigated, where x=(x_1,˙,x_n)^T is an unknown vector function. The system is considered in the most general setting and under weak assumptions about the entries of matrices A_k and delays h_k. The main result on uniform exponential stability is universal in the sense that it generates a set of 2^m-1 independent explicit statements (that can depend on all delays) on uniform exponential stability. The advantages over the existing results are demonstrated. The main tools employed by this article include the Bohl-Perron method, a priori estimates of solutions, and transformations of differential equations.

Original language | English |
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Pages (from-to) | 1537-1542 |

Number of pages | 6 |

Journal | IEEE Transactions on Automatic Control |

Volume | 67 |

Issue number | 3 |

DOIs | |

State | Published - 1 Mar 2022 |

## Keywords

- BohlâPerron (BP) method
- delay
- exponential stability
- linear differential system
- matrix measure
- stability test

## ASJC Scopus subject areas

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