Perturbations of Jordan Difference Systems

Abstract

In this brief chapter, we only consider perturbations of systems of difference equations with a single non-singular Jordan block. That is, we consider

$$\displaystyle{ y(n+1) = \left [\lambda I + N + R(n)\right ]y(n),\qquad \lambda \neq 0,\qquad N = \left (\begin{array}{cccc} 0&1&& \\ &0 &\ddots & \\ & &\ddots&1\\ & & &0 \end{array} \right )\,,\qquad n \geq n_{0}. }$$

(7.1)

Following the approach taken in Sect. 6.2, the next theorem can be considered as a discrete counterpart of Corollary 6.2, and its proof is parallel to the proof given in Theorem 6.1.