Stability criteria in terms of two measures for discrete systems

Abstract

This paper studies stability problems for two kinds of discrete systems in terms of two different measures. The basic idea of this approach is to discuss the qualitative behaviour of a map h along solutions of discrete systems whose initial value are measured by a second map h 0. By doing this, one may deal with, in a unified way, several concepts and associated problems, which are usually considered separately. Stability criteria in terms of two measures are established employing the method of Lyapunov functions and Razumikhin techniques.