Stability robustness in discrete-time multivariable feedback systems subject to noises and non-linear time-varying unmodelled dynamics is discussed. Based on the technique of functional analysis and the control algorithm advanced by Youlaet al., we derive a necessary and sufficient condition for robust stabilization as well as a closed-form solution to the problems of synthesizing optimal controllers that maximize the excess robustness to tolerate the unmodelled dynamics and noises. A necessary and sufficient condition for the solvability of such a robust stabilization problem is also introduced by means of Nevanlinna-Pick interpolation theory. In addition, an all-pass solution for the minimumH∞-norm problem is employed to treat our problems. Furthermore, neither the plant nor the controller has to be restricted to be stable or minimum-phase.