Stability conditions for linear delay difference equations: a survey and perspectives

Abstract

The paper presents an overview of the basic results and methods for stability investigations of higher-order linear autonomous difference equations. The presented criteria formulate several types of necessary and sufficient conditions for the asymptotic stability of the zero solution of studied equations, with a special emphasize put on delay difference equations. Various comments, comparisons, examples and illustrations are given to support theoretical results.

supported by the grant P201/11/0768
"Qualitative properties of solutions of differential equations and
their applications" of the Czech Science Foundation