Comparison of several stability conditions for linear difference equations

The paper compares the asymptotic stability criteria for linear difference equations, and some other well-known criteria found by the authors of the publication. Sufficient conditions given by the authors are better than the known ones. Criteria by the authors compete with the criteria of the Chinese researchers. The criteria of Kipnis and Komisarova consist of the linear constraints on the coefficients of the equations, while in the work of the Chinese researchers nonlinear conditions for asymptotic stability were found. There are domains in the space of positive coefficients of an equation, stability of which is revealed by the authors' criteria, but is not detected by the Chinese researchers test, and vice versa. The areas of guaranteed stability, which are revealed by different conditions, are shown for the linear difference equation with two delays. The classes of the difference equations are given in which the Kipnis and Komissarova criteria are certainly better. The corresponding theorems are proved. Examples illustrating the possibilities of using various criteria are given.