Asymptotic stability of nonlinear discrete dynamical systems involving (sp) matrix

Abstract

In this paper, we prove a  new result for the exponential stability of the null solution of a nonlinear  non-autonomous discrete dynamical system described by $$x(n+1)= g(n, x(n)) \qquad n = 0,1,2,...$$ where $g:Z^{+}\times \Omega \rightarrow \Omega$, $\Omega \subset R^k$ is a continuous nonlinear function satisfying $g(n, 0) = 0 \hspace{2mm} \forall n $, using the concept of (sp) matrix introduced by Xue and Guo. Numerical examples are also given to illustrate our result.