Numerical radius for the asymptotic stability of delay differential equations

Abstract

In this note, we make use of the numerical radius to investigate the asymptotic stability of linear systems of delay differential equations. We present examples to illustrate our assumption is weaker than the classical ones.

Keywords:

• Delay differential equations
• asymptotic stability
• numerical range
• numerical radius
• matrix norms

AMS Subject Classifications:

• 15A09
• 65F20

Acknowledgements

The authors would like to thank Professor Yiu-Tung Poon and the referee for their valuable suggestions which help us to improve the manuscript.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [grant number 11271084]; International Cooperation Project of Shanghai Municipal Science and Technology Commission [grant number 16510711200].