Discontinuous piecewise-linear discrete-time dynamics - maps with gaps in electronic sysems

Many important electronic systems are modelled by discrete-time equations with nonlinearities that are discontinuous and piecewise-linear, often arising as a result of quantization. Approximations based on linearization – the standard engineering response to nonlinearity – are often quite unhelpful in these systems, because of the form of the nonlinearity. Certain methods and results have been developed over a number of years for the analysis of discontinuous piecewise-linear discrete-time dynamics. The aim of this tutorial paper is to review that body of knowledge, and to show how it can be applied to representative electronic systems.