Acta Mathematica Vietnamica
Search within journal
Volumes and issues
Lyapunov Functionals that Lead to Exponential Stability and Instability in Finite Delay Volterra Difference Equations
Catherine Kublik , Youssef Raffoulpp. 77-89
Abstract
We use Lyapunov functionals to obtain sufficient conditions that guarantee
exponential stability of the zero solution of the finite delay
Volterra difference equation
$$
x(t+1) = a(t)x(t)+\sum^{t-1}_{s=t-r}b(t,s)x(s).
$$
Also, by displaying a slightly different Lyapunov functional we obtain conditions that guarantee the instability of the zero solution.
The highlight of the paper is the relaxing the condition $|a(t)| <1.$
Moreover we provide examples in which we show that our
theorems provide an improvement of some recent results.