Mixed H2 and H∞ optimal robust control design

This paper introduces a design methodology for a dynamic compensator that simultaneously minimizes the upper bound of a quadratic performance index and the H∞-norm of a disturbance transfer function matrix of a multiple-input/multiple-output system whose model contains parameter uncertainty in the state and input matrices. The real parameter uncertainty is modelled as additional measurement outputs and as additional weights on the existing noise inputs and measurement outputs of the system. The compensator equations are derived by taking the dual of a system with parameter variation in the state and output matrices, for which the compensator equations have previously been derived, and then taking the dual of the compensator equations. An algorithm for applying this theory is given and an example is shown.