New stability conditions for linear difference equations using Bohl-Perron type theorems.

The Bohl-Perron result on exponential dichotomy for a linear difference equation[image omitted] states (under some natural conditions) that if all solutions of the non-homogeneous equation with a bounded right hand side are bounded, then the relevant homogeneous equation is exponentially stable. According to its corollary, if a given equation is close to an exponentially stable comparison equation (the norm of some operator is less than one), then the considered equation is exponentially stable. For a difference equation with several variable delays and coefficients we obtain new exponential stability tests using the above results, representation of solutions and comparison equations with a positive fundamental function. [ABSTRACT FROM AUTHOR]