Robust disturbance attenuation with stability for linear systems with norm-bounded nonlinear uncertainties

In this paper, the problem of robust stabilization and robust disturbance attenuation is investigated for systems with linear nominal parts and norm-bounded nonlinear uncertainties on both states and control inputs. It is shown that the type of nonlinear uncertainty sets considered in this paper has an equivalent representation by linear uncertainty sets. Based on this key result and some standard Riccati inequality approaches for robust control of linear uncertain systems, a constructive design procedure is developed.