Nonlinear feedback vs. linear feedback for robust stabilization

The relative merits of nonlinear feedback over linear feedback are investigated in the context of certain robust stabilization problems. In particular an absolute tight computable bound on the radius of unmodeled dynamics against which robust stabilization is possible using nonlinear (adaptive) feedback is presented. This is used to compare nonlinear and linear feedback for robust stabilization. A nonlinear/linear tradeoff ratio is developed to quantify this comparison. The results support the view that nonlinear feedback is of significant advantage in situations where the plant exhibits significantly more parametric modeling uncertainty than dynamic modeling uncertainty