Synthesis of reduced-order H∞ controllers based on conjugation

A new state-space characterization of solutions of a class of model-matching problem (the so-called model-matching problem of the first kind by Limebeer) has recently been derived by Kimura based on the notion of conjugation (Kimura 1989 b). The results are extended to a more general case (still restricted to the problem of the first kind) and applied to the H∞ control problem. It is shown that the controller has a very simple structure with its order being identical to the plant order. To obtain a controller, we only need to solve two eigenvalue problems of size n and two Lyapunov-type equations of the same size, where n is the plant order.