This note considers the problem of stability robustness with respect to a c
lass of nonlinear time-varying perturbations which are bounded in a compone
nt-wise rather than aggregated manner. A family of robustness bounds is par
ameterized in terms of a nonsingular symmetric matrix. It is shown that the
problem of computing the largest robustness bound over the set of nonsingu
lar symmetric matrices can be approximated by a smooth minimization problem
over a compact set. A convergent algorithm for computing an optimal robust
ness bound is proposed in the form of a gradient flow.