On the nonlinearly structured stability radius problem

This paper considers the problem of finding a perturbation matrix with the least spectral norm such that a matrix-valued function becomes singular, where the dependence of the function on the perturbation is allowed to be nonlinear. It is proved that such a problem can be approximated by a smooth unconstrained minimization problem with compact sublevel sets. A computational procedure proposed based on this result is demonstrated to be effective in both linear and nonlinear cases.