On quadratic stability of systems with structured uncertainty

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