Conjugation and H∞ control of discrete time systems

The authors establish a conjugation notion for discrete-time systems. In discrete-time systems, conjugation is a very elementary operation on the rational transfer function that replaces some of its 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 optimal solutions of the H^∞ model-matching problem is reduced to a Lyapunov-type equation. It is further proved that the J-lossless conjugation of the model-matching problem is a natural state-space representation of classical interpolation in discrete time systems