Nonlinear Versus Linear Control in the Absolute Stabilizability of Uncertain Systems with Structured Uncertainty

This note considers a stabilization problem for a class of uncertain linear systems containing structured uncertainty described by a certain Integral Quadratic Constraint. The notion of stabilizability considered is that of absolute stabilizability. The main result gives a necessary and sufficient condition for the absolute stabilizability of this class of uncertain systems in terms of the existence of a solution to a corresponding “diagonally scaled" H°° control problem. It follows from this result that absolute stabilizability via nonlinear control implies absolute stabilizability via linear control.