Abstract
We establish conjugation notion in discrete-time systems, first introduced into the H ∞ control theory of continuous-time systems by Kimura (1989). In discrete-time systems, conjugation is a very elementary operation on rational transfer functions that replaces some of their poles by their reflections with respect to the unit circle. With the aid of J-lossless conjugation conjugation by a J.lossless system), it is shown that the parametrization of sub-optimal solutions of H ∞ model-matching problems is reduced to a Lyapunov-type equation. The parametrization of all solutions is given in an extremely simple way. It is further proved that the J-lossless conjugation of the H ∞ model-matching problem is a natural state-space representation of classical interpolation in discrete-time systems.
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