The robust regulation problem with robust stability

Among the most common purposes of control are the tracking of reference signals and the rejection of disturbance signals in the face of uncertainties. The related design problem is called the `robust regulation problem'. Here we investigate the trade-off between the robust regulation constraint and the requirement of robust stability. We first formulate the robust regulation problem as an interpolation problem, and derive from this a number of simple necessary conditions for the robust regulation problem to be solvable with a given stability margin. Then we show that these conditions are also sufficient provided the given stability margin is achievable at all.