In this project we will apply certain theories and techniques of nonlinear systems, in order to develop a fundamental and rigorous understanding of nonlinear discrete feedback systems with discontinuities. A typical example of these systems is the class of EA modulators, which are increasingly widely used in signal processing applications from consumer electronics to advanced communications. A new theory is needed for the analysis of such systems, which will describe rigorously their behaviour. Specifically, we will continue the investigation of the dynamic behaviour of these systems, extending the techniques used in the study of special systems with constant input, to systems with time-varying inputs. Symbolic dynamics are going to play an essential role in this attempt, providing us with a good theoretical descriptive tool and finally the study of the stability of these systems will be based on the extension of some certain nonlinear tools, such as Lyapunov functions, limit sets and higher prolongations.