Advances in Difference Equations (May 2017)
Stability of delay differential equations via delayed matrix sine and cosine of polynomial degrees
Abstract
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.
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