Performance robustness of discrete-time systems with structured uncertainty

Given an interconnection of a nominal discrete-time plant and a stabilizing controller together with structured, norm bounded, nonlinear/time-varying perturbations, necessary and sufficient conditions for robust stability and performance of the system are provided. This is done by first showing that performance robustness is equivalent to stability robustness in the sense that both problems can be dealt with in the framework of a general stability robustness problem. The resulting stability robustness problem is next shown to be equivalent to a simple algebraic one, the solution of which provides the desired necessary and sufficient conditions for performance/stability robustness. These conditions provide an effective tool for robustness analysis and can be applied to a large class of problems. In particular, it is shown that some known results can be obtained immediately as special cases of these conditions