Quadratic stabilizability and proper controllers

The problem of quadratic stabilization of systems with norm-bounded time-varying uncertainties via dynamic output feedback control is considered It is shown that a proper controller does not provide any profit compared to a strictly proper one, from a quadratic stabilization point of view. The quadratic stabilizing full order proper controllers are then characterized via the positive definite solutions of two parameter dependent Riccati equations. Finally, a thorough description of the associated numerical procedure is given