An upper bound for the complex structured singular value related to a linear time-invariant system over all frequencies is given. It is in the form of the spectral radius of the ${\cal H}_\infty $-norm matrix of SISO input-output channels of the system when uncertainty blocks are SISO. In the case of MIMO uncertainty blocks the upper bound is the $\infty $-norm of a special non-negative matrix derived from ${\cal H}_\infty $-norms of SISO channels of the system. The upper bound is fit into the inequality relation between the results of $\mu $ and $\ell _1$ robustness tests.