Stability of delay differential equations via delayed matrix sine and cosine of polynomial degrees

Advances in Difference Equations

Wei Wei¹  Chengbin Liang¹  JinRong Wang² 

[1] College of Mathematics and Statistics, Department of Mathematics, Guizhou University, Guizhou, P.R. China;College of Science, Guizhou Minzu University, Guiyang, P.R. China

关键词: finite time stability;    delay differential equations;    delayed matrix sine and cosine of polynomial degrees;   

DOI  :  10.1186/s13662-017-1188-0

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, we study the finite time stability of delay differential equations via a delayed matrix cosine and sine of polynomial degrees. Firstly, we give two alternative formulas of the solutions for a delay linear differential equation. Secondly, we obtain a norm estimation of the delayed matrix sine and cosine of polynomial degrees, which are used to establish sufficient conditions to guarantee our finite time stability results. Meanwhile, a numerical example is presented demonstrating the validity of our theoretical results. Finally, we extend our study to the same issue of a delay differential equation with nonlinearity by virtue of the Gronwall inequality approach.

【 授权许可】

CC BY