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Abstract: This paper is devoted to the stability analysis of a delay difference system of the form , , where a, b and c are real numbers and k is a positive integer. We establish some exact conditions for the zero solution of the system to be asymptotically stable. [Copyright &y& Elsevier]

Abstract: In this paper we are concerned with the exponential asymptotic stability of the solution of a class of differential equations with state dependent delays. Our approach is based on the Crandall–Liggett approximation and the properties of semigroups. [Copyright &y& Elsevier]

In this paper we study stability and asymptotic behaviour of a real two-dimensional system x′(t)=A(t)x(t)+B(t)x(t−r)+h(t,x(t),x(t−r)), where r>0 is a constant delay, A, B and h being the matrix functions and the vector function, respectively. The method of investigation is based on the transformation of the considered real system to one equation with complex-valued coefficients. Stability and asymptotic properties of this equation are studied by means of a suitable Lyapunov–Krasovskii functional. [Copyright &y& Elsevier]