Robust stability under simultaneous perturbations of linear plant and controller

The authors study robust stability under simultaneous plant and controller perturbations. A nominal feedback system must be robustly stable in the face of either the plant perturbations or the controller perturbations, so that it is robustly stable under the combined perturbations. Hence, the admissible controller perturbations can be defined by a Youla parameterization based on the nominal feedback system. This also applies to the set of admissible plant perturbations. From these two Youla parametrizations a sufficient condition is provided for robust stability under simultaneous perturbations. An example is provided in which this condition is less conservative than a similar condition conceived in terms of the gap metric