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This paper introduces an induced-norm formulation of a mixed /spl Hscr//sub 2/ and /spl Hscr//sub /spl infin// performance criterion. It is shown that different mixed /spl Hscr//sub 2/ and /spl Hscr//sub /spl infin// norms arise from different assumptions on the input signals. While most mixed norms can be expressed explicitly using either transfer functions or state-space realizations of the system, there are cases where the explicit formulas are very hard to obtain. In the later cases, examples are given to show the intrinsic nature and difficulty of the problem. Mixed norm robust performance analysis under structured uncertainty is also considered in the paper.< >