Robustness of linear systems towards multi-dissipative perturbations

We consider the question of robust stability of a linear time invariant plant subject to dynamic perturbations, which are dissipative in the sense of Willems with respect to several quadratic supply rates. For instance, parasitic dynamics are often both small gain and passive. We reduce several robustness analysis questions to linear matrix inequalities: robust stability, robust H₂ performance and robust performance in presence of disturbances with finite signal-to-noise ratios