Asymptotic stability of linear non-autonomous difference equations with fixed delay

This paper studies the asymptotic stability of the linear non-autonomous difference equations with fixed delay. It is shown that the difference system is asymptotically stable if and only if the norm of the limit for the coefficient matrix is less than 1 under some conditions. Furthermore, the discretization of the pantograph equation by Runge–Kutta methods with variable stepsize is analyzed. Finally, some numerical experiments are made to demonstrate the main conclusions.