Normalized H_∞ controller reduction with a priori error bounds

This note describes an approach to the reduction of controllers for the normalized coprime factor robustness problem as well as the normalized H_∞ problem. It is shown that a relative error approximation of a coprime factor representation of any suboptimal controller leads to a stability guarantee and an upper bound on the performance degradation when the reduced order controller is implemented. When the approximation is performed on the controller generator, guaranteed a priori stability and performance bounds are obtained in terms of the synthesis Riccati equation solutions of the normalized H_∞ control problems.