Stability criteria for a class of linear differential equations with off-diagonal delays. (English) Zbl 1180.34082

Suzuki, Masakatsu; Matsunaga, Hideaki

Discrete Contin. Dyn. Syst. 24, No. 4, 1381-1391 (2009).

This paper is concerned with the following delay differential system with off-diagonal delays \[ \begin{aligned} x_1'(t)&= a_1x_1(t)+ b_1x_n(t-r_1),\\ x_2'(t)&= -a_2x_2(t)+b_2x_1(t-r_2),\\ & \qquad\vdots\\ x_n'(t)&= -a_nx_n(t)+b_nx_n(t-r_n),\end{aligned} \] where \(a_j, b_j\) are real numbers and \(r_j\) nonnegative real numbers for \(j=1,2,\dots,n\). By means of root-analysis of the characteristic equation of the above system the authors obtain criteria for the asymptotic stability of the zero solution of the system.

Reviewer: Panagiotis Ch. Tsamatos (Ioannina)

MSC:

34K20	Stability theory of functional-differential equations
34K06	Linear functional-differential equations

Keywords:

delay differential equations; asymptotic stability; off-diagonal delays characteristic equation.