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

Abstract 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