Nonlinear versus linear control in the absolute stabilizability of uncertain systems with structured uncertainty

This paper considers a stabilization problem for a class of uncertain linear systems containing structured uncertainty. The uncertainties in the system are described by a certain integral quadratic constraint which allows for a rich class of uncertainties including nonlinear dynamic time-varying uncertainty. The notion of stabilizability considered is that of absolute stabilizability. The main results show that the question of absolute stabilizability for the class of uncertain linear systems under consideration is equivalent to the existence of a solution to a corresponding “diagonally scaled” H^∞ control problem. A consequence of this result is the fact that absolute stabilizability via nonlinear control implies absolute stabilizability via linear control