Nonlinear versus linear control in the output feedback stabilization of linear systems with norm bounded uncertainty

The efficacy of nonlinear control in the quadratic stabilization of linear systems containing norm bounded uncertainty is considered. In particular, the author examines the quadratic stabilization of uncertain systems via dynamic output feedback control. It is conjectured that, if a linear system containing norm bounded uncertainty can be stabilized via nonlinear control, then it can also be stabilized using linear control. The main result of this work proves this conjecture for a class of uncertain systems containing a single scalar uncertain parameter