The robustness of discrete-time systems in the presence of norm-bounded linear time-varying and/or nonlinear perturbations is addressed. A general framework for dealing with stability as well as performance robustness of such systems is set up whereby an arbitrary number of perturbations can be treated simultaneously. It is shown that a performance robustness problem can in fact be converted to a stability robustness problem. In addition, it is demonstrated how a stability robustness problem can be reduced to a simple algebraic problem, one which can be easily solved providing necessary and sufficient conditions for stability/performance robustness. These conditions are simple to compute and thus provide an effective tool for robustness analysis which can handle a large number of perturbations with relative ease. Furthermore, it is shown how in certain important cases controllers with optimal robustness properties can be designed. Finally, some results for computing the A norm of stable rational functions are provided.